Taxes on Tax-Exempt Bonds

8/6/2019 Taxes on Tax-Exempt Bonds

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Taxes on Tax-Exempt Bonds∗

Andrew Ang†Columbia University and NBER

Vineer Bhansali‡

PIMCO

Yuhang Xing§Rice University

This Version: 6 March, 2007

JEL Classication: G12, G28, H20, H24Keywords: municipal bonds, income and capital gains tax,

de minimis boundary, public nance

∗We thank Rick Green, Gur Huberman, Dan Li, Bob McDonald, and Andrew Schmidt for helpful

discussions. We are especially grateful to Jeff Strnad for providing detailed comments. We thank seminarparticipants at Brigham Young University, Columbia University, Rutgers University, UC Irvine, and UCSan Diego. We also thank Philippe Mueller for tabulating some of the data and Jihong Zang for checkingsome law sources.

†Columbia Business School, 3022 Broadway 805 Uris, New York, NY 10027. Ph: (212) 854-9154,Email: [email protected], WWW: http://www.columbia.edu/ ∼aa610.

‡PIMCO, 840 Newport Center Drive, Suite 100, Newport Beach, CA 92660. Ph: (949) 720-6333,Email: [email protected]

§Jones School of Management, Rice University, Rm 342, MS 531, 6100 Main Street, Houston, TX77004. Ph: (713) 348-4167, Email: [email protected].


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Taxes on Tax-Exempt Bonds

Abstract

Individuals must pay tax on the secondary market transactions of tax-exempt bonds. The protsinvolving changes in bond prices are taxed either as income or as a capital gain. We nd thatmunicipal bonds carrying market discount, which are subject to income tax, command higheryields than municipal bonds not subject to taxes arising from secondary market trades. However,the after-tax yields on municipal bonds with market discount are around 30 basis points higherthan yields on comparable municipal securities not subject to market discount taxation. Weestimate an implied tax rate of around 80% using trades of municipal bonds entering regions

where income tax rates apply.


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1 Introduction

The coupon payments and original issue discount (OID) of municipal bonds are exempt fromfederal income tax and are tax-advantaged nancial instruments for individual investors in hightax brackets. However, the prots from trading municipal bonds in secondary markets are tax-

able. These taxes are levied on capital gains or market discount and depend not only on thepurchase price of the bond, but also on the bond’s issue yield, issue price, and original maturity.While most municipal bond trades are not subject to tax, there is an important subset of munic-ipal bond transactions involving bonds subject to income tax. In some years these transactionsrepresent over 30% of all transactions. If individuals are the marginal agents in municipal mar-kets, municipal securities subject to tax should trade at higher yields to compensate individualsfor assuming the tax liabilities attached to these bonds, compared to municipal bonds with no

tax liabilities.Since 1993, accrued market discount is taxed at regular income tax rates. The Internal

Revenue Code (IRC) provides a de minimis exception, which allows small amounts of marketdiscount to be considered zero and be treated as capital gains. That is, below the de minimisboundary, accrued market discount is taxed as income. Above the de minimis boundary, bondsmay be subject to capital gains tax. If bonds are trading above par or accreted OID, all bondcashows are not subject to tax. Thus, investors face a discontinuous tax treatment from thesedifferent tax boundaries. In particular, bonds trading below the de minimis boundary are theleast attractive to individual investors as these bonds carry income tax liabilities, and thus thesebonds should carry the highest yields to compensate investors for bearing market discount tax-ation. In this paper, we study the effect of these no tax, capital gains tax, and income taxboundaries on municipal bond prices.

Municipal bonds are an excellent asset class to examine the effects of tax faced by individualinvestors. Individual investors hold over 70% of all municipal issues, which suggests that theyare likely to be the agents setting prices in these markets. In contrast, for other asset markets,

institutional investors are likely to dominate. For example, the de minimis rule also holds fortaxable Treasury and corporate bonds, but dealers and other nancial institutions are likely to setprices in these markets. In fact, Green and Ødegaard (1993) nd that after the 1986 tax reform,the marginal investor in Treasury bonds has a zero marginal tax rate. Thus, the municipal bonduniverse is a unique place to observe the effect of individual taxes on prices.

Our rst contribution is to demonstrate that taxes matter in determining the cross-sectional

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and time-series prices of tax-exempt bonds. We investigate how the tax law affects the relativepricing of municipal bonds with high tax liabilities. We show that these tax effects should betheoretically economically signicant by comparing the yields of municipal bonds subject totax with the yields of comparable municipal bonds that are fully tax exempt. We also nd thiseffect in data, so municipal bonds subject to tax command higher yields than fully non-taxablemunicipal securities.

However, the yields of municipal bonds with the highest tax burdens are higher than whatcan be explained with a present value model of bond after-tax cashows constructed using thezero-coupon municipal yield curve. Specically, investors purchasing these taxable municipalbonds in A-grade credit classes would obtain after-tax yields around 30 basis points higherthan yields on comparable securities not subject to tax. These high yields on municipal bondssubject to market discount taxation persist when taking only insured bonds and are especiallyhigh, over 60 basis points, for bonds with short 1-2 year maturities. Our results are also robust toconsidering bonds from the same serial issue trading above or below the de minimis boundary.

Our paper is related to Li (2006), who advocates that prices just below the de minimisboundary are dominated and should not be observed in theory. We especially focus on therst trades of bonds entering below de minimis territory because they reect a changing taxstatus of the bond and can be used to estimate changing implied tax rates priced by investors onthe same security. We show that the prices of bonds entering below de minimis territory have

very high implied tax rates. As bonds cross into regions where they are subject to income tax,bond prices decline as if an income tax rate of 79% applied, with priced tax rates as high as101% for interdealer trades. The largest after-tax yields occur for bonds trading deep below thede minimis threshold. Similarly, investors are also willing to give up large amounts of after-tax yield when bonds leave regions where they were subject to income tax. Thus, our resultssuggest that investors demand signicantly higher yields to hold below de minimis bonds thanwhat taxes seem to justify.

Our paper is related to a long literature that shows how taxes matter for asset prices (seePoterba, 2002, for a summary). Some of these papers address how municipal bonds are pricedrelative to other assets, like taxable Treasury debt, corporate securities, and equity securities(see, among many others, Auerbach and King, 1983; McDonald, 1983; and more recentlySialm, 2006). Another related literature examines how the spread in tax-exempt bond yieldsrelative to Treasury yields are affected by changes in tax law (see, among others, Poterba 1986,1989; Kochin and Parks, 1988; Fortune, 1996; Slemrod and Greimel, 1999; Brooks, 2002). Our

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approach and focus is very different from these papers because we document that taxes affectthe relative pricing of tax-exempt bonds themselves.1

The paper is organized as follows. Section 2 presents an overview of the tax treatment of gains in municipal bond transactions. We describe the data and the benchmark yield curve inSection 3. Section 4 contains the main results and shows that below de minimis bonds do carryhigher yields than other municipal bonds, but these yields are higher than what the zero-couponyield curve justies. Finally, Section 5 concludes.

2 Income and Capital Gains Taxes on Municipal Bonds

We use the term “municipal bonds” to describe all tax-exempt bonds, which includes bonds is-sued by municipalities, counties, states, other government authorities, and other entities entitled

to issue tax-exempt debt. The interest paid on municipal bonds is not subject to income taxlevied by the federal government, but may be subject to state income tax if an investor holdsmunicipal bonds issued by states where the investor is not considered to be a resident.2 Specif-ically, IRC § 103(a) exempts any interest received from municipal bonds for all taxpayers asnot counting towards gross investment income that is subject to federal tax. Consistent with theprinciple that interest on municipal bonds is not taxed, OID is not taxable and the amortizationof original issue premiums cannot be deducted. This tax treatment of initial issue premium is

consistent with the tax exemption of OID, since a municipal issuer can always change the initialissue price and coupons in opposite directions to produce the same issue yield.

1 A large outstanding puzzle is that the spread of Treasury yields to municipal bond yields declines at longmaturities. This effect is still unexplained, but many common explanations like default risk can be ruled out (seeChalmers, 1998). Green (1993) proposes that the raw Treasury yield is not the right benchmark and constructs arisk-free portfolio of taxable Treasury bonds so that income is transformed and treated as capital gains. However,McDonald (2006) notes that IRC § 1258 enacted in 1993 requires that coupon interest on Treasury debt in Green’stransaction must be reported as income. Of course, this puzzle persists in both the pre-1993 and post-1993 periods.Our study does not directly address this issue because it focuses only on the tax effects involving the pricing of

municipal bonds relative to other municipal bonds.2 The federal tax-exemption of state and local bonds originally had a constitutional basis, as afrmed by theSupreme Court in 1895 in the case of Pollack v. Farmers’ Loan and Trust Company . But, in 1988, the SupremeCourt overturned the constitutional basis for the tax exemption inSouth Carolina v. Baker , so the tax exemptionof municipal bonds is not protected by the U.S. constitution but now rests with Congress. Recently, in September2006, the Kentucky Supreme Court declined to review the decision of the Kentucky Court of Appeals that taxingout-of-state bonds, but not in-state bonds, violated the commerce clause of the U.S. constitution (Article I, Sec. 8,cl. 3). The Supreme Court is yet to rule on this issue.

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However, while the coupons paid by municipal bonds are tax-exempt, an investor may payfederal income or capital gains tax when a municipal bond is purchased or sold in the secondarymarket, just as in the case of a sale of a taxable Treasury or corporate bond. That is, while OID isnon-taxable, discounts arising from market transactions are taxable. In our analysis, we do notconsider the effect of state taxes on municipal bonds, or in effect, we assume that the marginalinvestor in a particular state’s bonds is an individual who is a resident of that state (see Cole,Liu and Smith, 1994). Our focus is on the effect of federal income and capital gains taxes onmunicipal bonds faced by a person purchasing a tax-exempt bond in the secondary market.

Investors must pay income tax on any municipal bond purchased or sold with market dis-count. According to current tax law (IRC § 1278(a)(2)(A)), market discount is created when apar bond trades for a price less than par, or an OID bond is sold at a discount to the accruedvalue of the OID. Bonds with less than one year of maturity are considered to have no mar-ket discount. Prior to 1 May, 1993, market discount was treated as a capital gain. Under theRevenue Reconciliation Act of 1993, accreted market discount is now taxed as ordinary incomeat the time a bond is sold or redeemed (IRC § 1276(a)(1)). To explain the taxation of marketdiscount, we rst show how market discount is computed for a par bond. Then, we consider thecases of a premium and an OID bond.

2.1 Case of a Par Bond

First, consider a bond of par value $100 with an original 10-year maturity, paying semi-annualcoupons of 10%. We refer to this bond as Bond A. Suppose that two years after issue, witheight years to maturity, Bond A trades at a price of $95. The market discount on this bondis 100 − 95 = $5. If the bond is held to maturity, the investor owes ordinary income taxon $5, which is paid when the bond matures. For the investor purchasing Bond A, only thenal cashow of the bond is affected, because the investor pays no tax on the coupons of themunicipal bond.

The tax code provides a de minimis exception in IRC § 1278(a)(2)(C), which states:

If the market discount is less than 14 of 1 percent of the stated redemption price of

the bond at maturity multiplied by the number of complete years to maturity (after

the taxpayer acquired the bond), then the market discount shall be considered to be

zero.

This de minimis rule mandated by legislation imposes a discontinuity between income and

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capital gains tax rates at the de minimis cut-off. The de minimis boundary is deterministic andis specic to each bond.3

Applied to our example, the de minimis boundary of Bond A is100(1 − 0.0025 × 8) = $98

at timet = 2 as Bond A has eight complete years to maturity. Thus, if Bond A trades for$98.50, say, two years after issue, then this price is above the de minimis boundary and Bond Ais considered to have no market discount. If the investor holds Bond A to maturity, the investorwould pay capital gains tax on100 − 98.50 = $1.50 when Bond A matures. Again, like themarket discount case, only the nal cashow of the bond is affected.

Naturally, since the top federal income tax rate is currently 35%, which is higher than thecurrent long-term capital gains rate of 15%, once a bond crosses the de minimis boundary, itbecomes subject to a more onerous tax treatment. This decreases the cashows received bythe purchaser of the bond. In particular, the bond price should jump discretely downwards asthe bond price falls through the de minimis boundary to maintain the same after-tax yield tothe purchaser of the bond. Similarly, as a bond pushes upwards through de minimis, the nalcashow to the bond purchaser increases, and the value of the bond rises. This effect can bealso be interpreted in duration terms: bonds lying near the de minimis boundary have higherdurations than what a simple pricing model without tax effects would predict. Around the deminimis boundary, straight bonds have negative convexity. We refer to bonds trading belowthe de minimis threshold as below de minimis bonds. Suppose that individual investors are the

marginal investors in municipal bond markets. Then, since below de minimis bonds are subjectto income tax, these bonds should trade at lower prices and higher yields than bonds tradingabove the de minimis boundary to compensate individuals for bearing these tax liabilities.

2.2 Case of a Premium Bond

Municipal bond premiums as a result of secondary market transactions are not deductible underIRC § 171(a)(2), but capital gains are subject to tax.4 This asymmetry in the tax law means that

a premium bond has the same tax treatment as a par bond. Thus, for a par or premium bond,3 There is no tax asymmetry for investors selling bonds with market discount to deduct a capital loss. Consider

an investor holding a par bond from issue for longer than a year. Selling at a price above par generates a taxablecapital gain and selling at a price below par generates a deductible capital loss. Capital gains rates apply in boththese transactions for the seller. The asymmetric tax treatment applies only to the purchaser of a bond.

4 A holder must amortize the premium on a municipal bond under IRC § 1.171-1(c)(1) for reporting purposesand to determine the adjusted basis in the bond, but these are not deductible for individuals under current tax law,unlike taxable bonds (see IRS Publication 550).

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there are two important tax boundaries. Above par, all the bond cashows are not subject to tax.The area below par to the de minimis boundary subjects the difference between the purchaseprice and par value to capital gains tax. Below de minimis bonds purchased in the secondarymarket have market discounts that are taxed at income tax rates. For bonds originally issuedat discount, there are also two important tax regions, but since the bond is not issued at par,the bounds need to be changed to take into account the effect of the OID. We now discuss thetreatment of OID bonds.

2.3 Case of an OID Bond

Computing market discount for an OID bond is more complicated than computing market dis-count for par or premium bonds. In the case of dening market discount on an OID bond, IRC

§ 1278(a)(2)(B) replaces the stated redemption price of the bond at maturity by the revised issueprice. Thus, for a bond originally issued at discount, market discount is dened as the differ-ence between the purchase price of a bond and the original issue price of the bond plus accretedOID. From issue date to maturity, OID accretes according to the constant yield accrual method(IRC § 1272-1(b)).5 Since OID is original interest, it is not taxable for a municipal bond, andthus the accretion of OID as the bond matures is also not taxable. Market discount is createdwhen an OID bond trades at a price below the bond’s original issue price plus accreted OID.The original issue price plus accreted OID is termed the revised issue price (IRC § 1278(a)(4))and can be computed as the present value of the remaining cashows of the bond discounted atthe bond’s original issue yield.

As an example, consider Bond B, which is an OID bond originally issued with a 10-yearmaturity paying a 10% semi-annual coupon. Bond B was issued at a price of $88.5301 with apar value of 100. The semi-annual initial yield at issue of this bond is 12%. Figure 1 illustratesthe accreted OID of this bond in the convex solid line. At any point in time, the revised price of the bond is the value of the remaining payments of the bond discounted at its original 12% yield.

Suppose that at year 2, an investor buys Bond B at a price of $84. With eight years remaining,the revised issue price of the bond is the discounted value of 16 coupons of $5 received at 6-month intervals at a yield of 6% every six months. This revised issue price is $89.8941, whichis equivalent to the original issue price of $88.5301 plus $1.3640 in accreted OID. The market

5 For bonds issued prior to 27 September, 1985, straight line amortization (or the ratable accrual method) canbe used. An investor would never rationally choose straight line amortization because the constant yield methodleads to a slower accrual of the market discount.

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discount att = 2 is the difference between the revised issue price and the purchase price, whichis 89.8941 − 84.0000 = $5.8941. This is shown in Figure 1 as the solid vertical line att = 2 .If the investor holds Bond B to maturity, the market discount of $5.8941 is taxed at income taxrates when the bond matures att = 10 .

An alternative way to view the calculation of market discount is as follows. According tothe original OID schedule of Bond B fromt = 2 to maturity att = 10 , Bond B should increasein price from $89.8941 to $100.0000. This increase of 100.0000 − 89.8941 = $10.1059 in theOID schedule is tax exempt. If Bond B is purchased att = 2 for $84 and held to maturity,then a portion of the100 − 84 = $16 gain is tax-free because some of this increase would havehappened under the original accrual schedule. Only the gain in excess of the accreted OID istaxable. Thus, the taxable gain, which is considered income, is100 − 84 − 10.1059 = $5.8941,and the income tax on $5.8941 is payable at maturity if the bond is held to maturity.

The de minimis boundary for Bond B is still dened relative to the stated redemption priceof the bond. Thus, the de minimis boundary for Bond B att = 2 is89.8941− 100× 0.0025× 8 =

$87.8941. In Figure 1, we graph the de minimis boundary in black dots below the accreted OIDsolid line. Any trade above the de minimis level is considered to have no market discount. Thus,if Bond B trades att = 2 for a price greater than $87.8941, then the gain is considered to bede minimis and there is no market discount, but the gain may be subject to capital gains tax.For example, suppose that Bond B’s price att = 2 is $89. The investor would see a gain of

100− 89 = $11 if Bond B is held to maturity, and $10.1059 of this gain is tax-free according toBond B’s accreted OID schedule. Thus, if held to maturity, the investor would pay capital gainstax on100 − 89 − 10.1059 = $0.8941 when Bond B matures.

As a nal case, suppose that Bond B is trading above its accreted OID schedule. For ex-ample, suppose that att = 2 , Bond B trades for $91, which is greater than the revised price of Bond B of $89.8941. An investor buying Bond B and holding it to maturity would see a gain of 100 − 91 = $9, but none of this is taxable since under the OID accretion schedule, the investoris entitled to a tax-free gain of 100 − 89.8941 = $10.1059 from t = 2 to t = 10 . Thus, theaccreted OID acts as a bound below which the OID bond becomes subject to tax, at least atcapital gains rates. In addition, if the bond price is below de minimis, the market discount istaxed at income tax rates.

Thus, we can summarize the three areas with different tax treatments for an OID bond heldto maturity in the following table:

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Region Bound Tax Treatment

No-Tax Region P ≥ RP All cashows tax-exempt

Capital Gains Tax RegionDM < P < RP No market discount(RP − P ) is taxed at capital gains rates

Income Tax Region P ≤ DM Market discount exists(RP − P ) is taxed at income tax rates

We denote the revised issue price of the bond asRP , the purchase price of the bond asP , andthe de minimis boundary asDM . The par and premium bonds can be mapped into this tablebecause for these bonds, the revised price of the bond is always par value, that isRP = par.The payment of tax occurs at maturity if the bond is held to maturity.

We denote the tax-exempt region where the bond is trading above the revised price of thebond as the “No-Tax Region,” which occurs for a par or premium bonds trading above parvalue and an OID bond trading above the revised price. The second boundary is the de minimis(DM ) bound. Bonds trading between the de minimis boundary and the revised price are subjectto capital gains. We refer to this as the “Capital Gains Region.” As bonds decrease further inprice to trade below de minimis in the “Income Tax Region,” they become subject to incometax.

2.4 Computing Municipal Bond Prices

The Tax-Exempt Yield

We follow Rule G-33 of the Municipal Securities Rulemaking Board to compute municipalbond prices.6 Since we only consider bonds with at least one year to redemption (as marketdiscount only applies to bonds with maturities greater than one year), the price of a municipalbond on $100 par value is given by:

P =N

n =1

100 × C/ 2(1 + Y/2)n − 1+ w +

100(1 + Y/2)N − 1+ w −

A360

100 × C, (1)

whereY is the semi-annual yield-to-maturity of the bond;C is the semi-annual coupon rateimplying a six-month coupon rate of C/ 2 every six months; andN is the number of remaining

6 Available at http://www.msrb.org/msrb1/rules/ruleg33.htm

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coupon payments occurring at 6-month intervals. The fractionw is dened as:

w =180 − A

180,

whereA is the number of accrued days from the beginning of the interest payment period to thesettlement date. We follow the 30/360 convention in the municipal bond market to computeA,so we count 30 days for each complete month to make 180 days in each interest rate period and360 days in one calendar year. The yieldY is often called the tax-exempt yield because it is theyield computed on tax-exempt municipal bonds. We refer toY as the “yield.”

In equation (1), the fractionw accounts for the accrued interest on the bonds. For a bondvalued on a date when an interest payment is received,w = 0 and the bond has no accruedinterest. The rst two terms in equation (1) calculate the present value of all cashows of thebond, including accrued interest. The last term in equation (1) subtracts accrued interest. The

accrued interest is added on the bond conrmation at settlement to compute the total amountdue.

The After-Tax, Tax-Exempt Yield

The yield,Y , does not take into account the taxes that must be paid by an investor purchasing amunicipal bond in the secondary market. To adjust for taxes, we dene an “after-tax yield,”Y τ ,on municipal bonds, assuming that the bonds are held to maturity. Using the same notation as

equation (1), we implicitly deneY τ to solve:

P =N

n =1

100 × C/ 2(1 + Y τ / 2)n − 1+ w +

100 − tax(1 + Y τ / 2)N − 1+ w −

A360

100 × C, (2)

where tax is the appropriate tax payment payable at maturity, which is given by:

tax =

0 if P ≥ RP

τ C × (RP − P ) if DM < P < RP

τ I × (RP − P )if

P ≤ DM ,

(3)

for RP the revised price of the bond,τ C the capital gains rate, andτ I the income tax rate.The de minimis boundary is given byDM = RP − 100 × 0.0025 × oor(N/ 2). The numberof complete years of maturity is given by oor(N/ 2), where oor(·) rounds the number of remaining cashows downwards to the nearest integer. In equations (2) and (3), taxes reducethe nal cashow, and hence increase the after-tax yield, for bonds trading below the revisedprice. Taxes only affect the last cashow of the bond as the bond coupons are exempt from tax.

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In computing the after-tax yield, we assume that the income tax rate and the capital gains rateapplied at maturity are the top marginal federal tax rates in the year of the trade. For example, atrade in 2006 would useτ I = 0 .35 andτ C = 0 .15. These rates have changed across our sampleand start atτ I = 0 .396 andτ C = 0 .28 in 1995.7 Municipal bonds do respond to perceptions of future, and actual, changes in tax rates (see, for example, the summary of Fortune, 1996) andagents may anticipate future changes in the tax schedule. We also compute the tax rates impliedfrom secondary market trades using equation (2). These can be identied by bonds crossing thede minimis boundary and changing their tax rates fromτ I to τ C or vice versa.

2.5 Other Issues

In our exposition, we considered only the effect of capital gains and income taxes on municipal

bonds for the case where a bond is held to maturity, similar to the literature estimating impliedtax rates on bond prices like Litzenberger and Rolfo (1984) and Green and Ødegaard (1993).In Appendix A, we discuss the tax treatment of bonds sold before maturity. This issue becomesimportant because the timing of the tax payment occurs the sooner of when the bond maturesor when the bond is sold. Even if investors believe that the expected holding period return on amunicipal bond is constant, investors may have an incentive to sell early if there is a tax benetfrom accelerating the payment of the market discount tax, rather than postponing it to maturity.

For an investor buying a par or a premium bond, there is no ex-ante incentive for that investorto sell the bond early assuming that the expected return on the bond is equal to its purchase yield(or a version of the Expectations Hypothesis [EH] holds for purchasing that municipal bond).While the EH is rejected for Treasury yields, theR 2 s of predictability regressions are typicallyvery low (see Campbell and Shiller, 1991), and it is not clear that individual investors are ableto successfully market time in the municipal bond market to take advantage of these deviationsfrom the EH.8 Early evidence by Brick and Thompson (1978) nds that lagged Treasury yieldsdo not predict long-term municipal yields. However, even if investors expect to receive the

purchase yield over the remaining maturity of the bond, there is an incentive for investors to sellan OID bond early because the accretion of OID at the issue yield is different from the accretionof discount at the purchase yield. In Appendix A, we show that this usually amounts to less than

7 These rates are available from the IRS. See, for example, http://www.irs.gov/formspubs/article/0„id=150856,00.html for the 2006 federal tax rate schedule.

8 Retail investors trying to time the market generally underperform aggregate market benchmarks in equitymarket trades (see, for example, Barber and O’Dean, 2000).

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one basis point in normal cases.The value of a municipal bond may also be affected by other issues not easily captured in

simple cashow discounting methods. Constantinides and Ingersoll (1984) and Strnad (1995),among others, demonstrate that the value of a bond should also be affected by the tax optionsthat trading the bonds allow to time the realizations of capital gains and losses. Chalmers(2000) notes that these effects are much less prevalent in the municipal bond market becausebond premium amortization cannot be deducted as an expense and municipal bonds cannotbe directly shorted (because only tax-exempt authorities and institutions can pay tax-exemptinterest).

Finally, unlike themarket for Treasury bonds, municipal bond markets aregenerally notveryliquid. Downing and Zhang (2004), Hong and Warga (2004), Green, Hollield and Schürhoff (2005), and Harris and Piwowar (2006), among others, nd large trading costs, especially forretail customers in the municipal bond market. We remove from our sample all transactionswith par amount traded below $10,000 to minimize these effects. Even after removing smalltrades, liquidity may still be an important determinant in pricing. To partially account for this,we treat inter-dealer transactions separately from dealer transactions with customers. We alsoseparately look at municipal issues only for California and New York issues. Municipal bondsfrom these states tend to be the most liquid, as noted by Biais and Green (2005), because thesestates have high income tax rates and have many residents with high marginal tax rates for

whom in-state municipal bonds are attractive investments. We will also match bonds tradingwith market discount with other bonds that have fully tax-exempt cashows on the basis of parvalue traded.

3 Data

In Section 3.1, we begin by showing that post-1992, individuals are the main holders of mu-nicipal bonds, holding over 70% of all outstanding municipal issues. Section 3.2 describes thedataset, consisting of 5,372,631 transactions from January 1995 to November 2005 on an A-grade credit quality sample of municipal bonds. To facilitate comparison of these bond prices,we construct a municipal bond zero-coupon curve each business day, which we describe inSection 3.3.

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3.1 Who Holds Municipal Bonds?

Figure 2 shows the main investors in municipal bonds from 1952:Q1 to 2006:Q1 broken downinto direct and indirect household investors, banks, and insurance companies. Indirect house-hold investment comprises mutual funds, closed-end funds, and money market funds. The

data is computed using the Flow of Funds data from the Federal Reserve by taking the variousamounts held by each investor class and dividing by the total number of municipal bonds out-standing each period. The amount of municipal bonds held by foreign investors and pensionfunds is very small (well below 1%) and is not shown.

During the 1970s and 1980s, banks were the main holders of municipal bonds becausethey were allowed to buy municipal securities, receiving tax-exempt income, and funded thesepurchases by issuing debt or borrowing for which they received a tax deduction of up to 80%

of the interest expense. This changed with the Tax Reform Act of 1986, which disallowedthe deduction for the carrying cost of purchasing tax-exempt municipal bonds. This causedthe holdings of municipal bonds by banks in Figure 2 to decline substantially from a highof 50% in the mid-1970s to below 10% by 2006.9 The other large institutional holders of municipal securities are insurance companies. Post-1992, insurance companies hold around12% of all municipal bonds. The proportion of municipal bonds held by insurance companieshas uctuated roughly between 10-20% since the 1950s, with a large drop from above 20% in1980 to slightly above 10% in 1986. During this period, the property and casualty insuranceindustry experienced large underwriting losses, which caused insurance companies to disinvestin municipal securities.

Since the early 1990s, individual investors are the main holders of municipal bonds andnow hold well above 70% of all municipal issues. Poterba and Samwick (2002) show that as ahousehold’s marginal tax rate increases, theprobability that a household holds tax-exempt bondsincreases and the portfolio share of a household’s wealth in municipal bonds also increases.This is not surprisingly because municipal bonds are tax-advantaged vehicles for individuals

with high marginal tax rates. Households can hold municipal bonds directly or indirectly. Atthe end of the rst quarter of 2006, individuals directly held 38.1% of all municipal securities

9 One incentive for banks continuing to hold municipal bonds is that under IRC § 265(b)(3)(B), banks candeduct 80% of the carrying cost of a bank-qualied municipal bond. The total volume of these bonds is smallas a bank qualied issuer can issue no more than $10 million of tax-exempt bonds in a given year. Most of these bank-qualied issues rarely trade in the secondary market. In our sample, fewer than 6% of all transactionsinvolve bank-qualied bonds. For a history of institutional developments in the municipal market, see Hildreth andZorn (2005).

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outstanding and held 33.6% through mutual funds, closed-end funds and other pass-throughintermediary vehicles. Thus, at the end of the rst quarter of 2006, individuals directly andindirectly held a total of 71.8% of all outstanding municipal bonds. In summary, since 1992,individuals have held substantial amounts of municipal bonds. This suggests that tax rates of individual investors may play a role in the relative pricing of municipal securities.

3.2 Municipal Bond Transactions Data

Our data on municipal bonds is the Municipal Securities Rulemaking Board (MSRB) dataset,which contains all transactions of municipal bonds involving municipal bond dealers registeredwith the MSRB. These trades are made available with a one-day lag through the Bond MarketAssociation and with a short lag of 15 minutes through data vendors such as Bloomberg and

Reuters. The MSRB database lists a price, a trade date, and the par value traded of each trans-action. From January 24, 1995 to August 25, 1998, only interdealer transactions are includedin the data. After August 25, 1998, all transactions between dealers and customers are recordedwith an indicator denoting whether the transaction is a sale or purchase.

Over our sample period from January 1995 to November 2005, the MSRB database contains58,791,805 individual transactions involving 1,974,798 unique municipal securities, which areidentied through a CUSIP number. The MSRB database contains only the coupon, dated dateof issue, and maturity date of each security. We obtain other issue characteristics for all themunicipal bonds traded in the sample from Bloomberg. Specically, we collect information onthe bond type (callable, putable, or sinkable, etc.); coupon type (oating, xed, or OID); theissue price and yield; the tax status (federal and/or state tax-exempt, or subject to the AlternativeMinimum Tax (AMT)); the size of the original issue; the S&P rating; and whether the bond isinsured. Our S&P rating is collected in May 2006, so the S&P rating is relevant at the time of maturity for bonds that have expired, or at May 2006 for current bonds at that time.10

In our analysis, we focus on bonds issued in the 50 states that are exempt from federal and

state income taxes not subject to the Alternative Minimum Tax (AMT). We take bonds rated byS&P with a rating of A- or higher, which we refer to as the “A-Grade” class of municipal bonds.

10 Neither S&P’s Ratings IQuery or Moody’s Ratings Delivery Service provide complete historical rating in-formation for public nance issues. Both these companies only provide past ratings changes for bonds that theycurrently cover. That is, for bonds that have defaulted, matured, or are no longer covered by analysts at S&P orMoody’s, past rating information on these individual bonds cannot be directly obtained from these companies.However, S&P and Moody’s do publish aggregate historical information on the default experience and transitionsbetween each credit class.

13



Over our sample period, there have been zero defaults in A-Grade municipals and the defaultsof investment-grade municipal bonds have been much lower than investment-grade corporatebonds (see studies on municipal defaults by, among others, Litvack and Rizzo, 2000; Woodell,Montrone and Brady, 2004).11 We take only straight bonds with maturities one to 10 yearsbecause market discount does not apply for bonds with less than one year of maturity and thereare relatively few straight bonds with maturities longer than 10 years. Bonds with very longmaturities often are issued with call or sinking fund provisions. We also do not take transactionswithin a month of issue because Green, Hollield and Schürhoff (2006) document signicantaftermarket effects on newly issued bonds. Appendix B contains a detailed descriptions of ourdata lters.

After merging our transactions data with the descriptive data and applying our data lters,we are left with a sample of 5,372,631 transactions on 259,471 unique securities. Thus, eachbond trades 21 times, on average, over our 11 year sample. A small fraction (5.65%) of issuestrade only once. In the top panel of Figure 3, we plot the total number of trades each month. Thelarge jump in the number of trades in August 1998 is due to the inclusion of all trades betweendealers and customers being added at this date. Prior to this date, only interdealer transactionsare recorded.

In the bottom panel of Figure 3, we plot the proportion of bond transactions each monthinvolving bonds trading below their de minimis boundaries. The gure also overlays the A-

grade 5-year zero-coupon yield. Naturally, as interest rates increase, bond prices decline andthe number of transactions involving bonds with prices below de minimis increases. This isclearly seen in the large spike of de minimis transactions (over 30%) taking place in 2000. In1998 and over 2001-2003 as interest rates decreased, the number of de minimis transactionsdecreases. Nevertheless, because of the large amount of transactions in our database, there arestill a sizeable number of de minimis trades in these years. For example, in 2002, there are12,803 transactions of below de minimis bonds, while there are 31,526 trades of bonds withprices below de minimis in 2003.

In Table 1, we report proportions of the unique CUSIPs (Panel A) and proportions of thetransactions (Panel B) falling into various categories. Panel A reports that Texas, California,

11 An alternative view is provided by Trzcinka (1982), who argues that the risk premium for municipal bonds ison average higher than corporates of the same rating. If true, this risk premium is not observed in ex-post defaultsof municipal versus corporate bonds of the same S&P rating. The famous defaults on the bonds of the WashingtonPublic Power Supply System and Orange County, California occurred in 1990 and 1994, respectively, before oursample starts in 1995.

14



New York, and Michigan are the states of origin having the largest proportions of bonds issued.Of the 259,471 unique bonds in our sample, only a minority (24.43%) of them are par bonds,most of them are general obligation bonds (48.71%) and approximately three quarters are ratedAAA by S&P and are insured.12

Panel B shows that of the 5,372,631 transactions of bonds, most of the trades involve bondsissued in California, New York, Texas, and Florida. Overall, the proportions of trades of eachstate correspond roughly to the proportions of bonds issued by those states. But, there are somestates like New York, whose share of trades (12.81%) is signicantly larger than the numberof unique CUSIPs (8.92%) of NY securities. Panel B shows that trades of discount bondsconstitute 35.67% of all trades, which is higher than the proportion of bonds issued at discount(30.83% in Panel A). This is unlike corporate and U.S. Treasury issues, which are issued almostexclusively at par.

The proportion of transactions from dealers to customers is 67.88% in our sample. Mostof these trades (43.42% of all trades) involve sales to customers from dealers at the ask. Themedian par amount traded is $50,000 with very large trades constituting over $1 million. Theremainder of trades (32%) are interdealer trades. The proportion of trades that are ask tradesor bid trades are different for transactions above or below the de minimis boundary. This indi-cates that the bid-ask spread may play a role for the potential different pricing effects of bondstrading above or below de minimis. For all the transactions above de minimis, the percentage

of ask, bid, and interdealer prices are 45.28%, 24.12%, and 30.60%, respectively, whereas thecorresponding proportions involving below de minimis bonds are 27.5%, 37.19%, and 35.31%,respectively. Hence, to minimize effects from possible bias resulting from the bid-ask spread,we treat bid, ask, and interdealer trades separately in our analysis.

In Table 2 we provide some further details on the distribution of original issue discountand premiums of our 259,471 bonds. Most bonds issued at discount are issued just slightlybelow par, but there are a large number of bonds issued at deep discount. For bonds issued atpremiums, many bonds (15% of all CUSIPs) carry substantial premiums of at least $5 abovepar. The large cross-section of original issue prices is important for our analysis because themain reason why bonds decline in price is through increasing interest rates, since the credit riskin our A-grade municipal bonds is negligible. Bonds issued at different prices will decline at

12 The main insurers are the Municipal Bond Insurance Association (MBIA), AMBAC Indemnity Corporation,Financial Security Assurance (FSA), and Financial Guaranty Insurance Company (FGIC), which are all rated AAAby S&P. These companies insure 20.49%, 16.13%, 13.03%, 12.98% of the bonds in our sample.

15



different amounts when interest rates rise. Thus, at a given time when interest rates have risen,the bonds trading below de minimis will not all have been issued at one particular point in time.This substantially reduces, but does not eliminate, the xed time effects of the dated dates of issue on our analysis.

3.3 Municipal Zero-Coupon Bond Curves

To provide a benchmark for all municipal bond trades, we construct a daily municipal zero-coupon yield using the trades of all municipal bonds in our A-grade sample. We follow themethod of Nelson and Siegel (1987), so the zero-coupon yield for maturityn half-years,r n , isgiven by:

r n = β 0 + ( β 1 + β 2 )1 − exp(− n/τ )

n/τ − β 2 exp(− n/τ ), (4)

which is determined by the parametersθ = {β 0 , β 1 , β 2 , τ }. We estimate these parameters dailyby tting the Nelson-Siegel curve to all the A-grade bonds traded each business day. In using allbonds, we bias all our results downwards because below de minimis bonds should have higheryields to compensate investors for the tax payments they must make.

For each transaction price, we use the zero-coupon rate implied by equation (4) to discountthe cashows of the bonds. This gives us a tted price for each bond,P , which we compute by:

P m =N

n =1

100 × C/ 2

(1 + r n / 2)n −1+

w+

100

(1 + r N / 2)N −1+

w−

A

360100 × C, (5)

where each cashow is discounted by the zero-coupon yield. We denote bond prices computedusing the tted zero yield curve as “model-implied” (or “zero-implied”) bond pricesP m withcorresponding “model-implied” yieldsY m . By denition,Y m is the yield implied by valuingthe bond cashows using the municipal zero-coupon yield curve on that trading day. Althoughstrictly speaking the zero yield curve is model-free, we use the term model-implied to denotethat it would represent fair value to a valuation model that would take as given, or t exactly,

the estimated term structure of municipal zero-coupon bonds. Model-implied yields are thetheoretical yields which would apply if the zero-coupon yield curve represents fundamentalvalue.

Each trading day, we estimate the parametersθ to minimize the distance between actualtransaction prices and the predicted prices using the zero curve:

minθ

i

(P mi − P i )2 , (6)

16



whereP mi is the price of bondi computed using the Nelson-Siegel zero-coupon curve in equa-tion (5) andP i is the transaction price of bondi. We take the summation over all bonds tradedeach day in our sample.13 We nd that the differences between actual yields and zero-impliedyields are very small, with the average difference between transactions yields and zero-impliedyields over all bonds for our sample being 2 basis points.

Figure 4 plots the time-series of our estimated municipal zero-coupon curves for maturitiesof 1, 5, and 10 years in the top two panels and the bottom left panel. Along with our estimates,we also plot the zero-coupon curve for municipal bonds from Bloomberg, which start in August2001. Bloomberg’s method of computing zero rate curves is not made public, but Bloomberg’ssample includes bonds with callable and sinking fund features. Bloomberg’s estimation samplealso relies on dealer quotations in addition to using transaction prices. Our zero-coupon ratesare slightly lower than the Bloomberg data, which is as expected because our sample excludesall bonds with embedded option features. Yields at the 1-year maturity hovered around 1% from1995 to 1999, and rose to 5% in 2000 before declining to 1% in 2003. At the end of our samplein November 2005, the 1-year zero municipal yield was around 3%. At the long end of the yieldcurve, 10-year zero yields have been much more stable, around 4-5% over 1995 to 2005. Thesetrends mirror the movements in Treasury yields.

In the lower right panel of Figure 4, we plot the average term structure of municipal zero-coupon rates over our sample from 1 to 10 years. It is a well-known stylized fact that municipal

yield curves have always been upward sloping (see Fabozzi and Feldstein, 1983). We ndthat our estimated zero yield curves are upward sloping in every trading day. The averageterm spread between 1- and 10-year zero-coupon yields is 1.27%. To compare this number tocoupon yields, we also plot the average par coupon yield curve implied from our zero yields.The corresponding par yield spread is 1.18%.

4 How Taxes Affect Tax-Exempt Bond Prices

In Section 4.1, we show that the theoretical effect of taxes on tax-exempt bond prices may belarge. We examine this effect in data in Sections 4.2 to 4.6. In Section 4.2, we show that yieldson below de minimis bonds are higher than what the zero curve predicts. Section 4.3 investigatesif empirical duration is responsible for this effect and also presents detailed controls for default

13 In our estimations of the zero curve, there are some bonds that trade more than once per day. For these bonds,there will be more than one trading price per day, but there is only one zero-curve implied model price.

17



risk and transaction size. In Section 4.5 we examine the effect of taxes on bonds crossing into,or out of, taxable regions. We estimate implied tax rates using bonds entering or leaving taxableregions in Section 4.6.

4.1 What the Effects of Taxes on Tax-Exempt Bonds Should Be

We now calibrate the effect of taxes on municipal bond prices. Taxes only affect the nalcashow of a municipal bond subject to tax, so it could be the case that since the tax paymentis small relative to the nal coupon and the return of principal, the effect of taxes on municipalbonds should also be small. This will be true under certain situations, but we now demonstratethat we should expect non-negligible tax effects for an average bond using a representativenumerical example.

Consider a $100 face value bond paying semi-annual coupons of rateC with a maturity of N/ 2 years. This bond was originally issued at par. If the current municipal yield curve is at atthe after-tax yieldy, then the price of this bond, assuming the bond is held to maturity, is givenby:

P = 1 −τ

(1 + y/ 2)N

− 1 N

n =1

100 × C/ 2(1 + y/ 2)n +

100 × (1 − τ )(1 + y/ 2)N , (7)

which is derived by rearranging equation (2). The bond priceP and the tax rateτ depend oneach other and must be solved jointly, with

τ =

0 if P ≥ 100

τ C if DM < P < 100

τ I if P ≤ DM

and the de minimis boundaryDM = 100(1 − 0.0025 × N/ 2). An investor buying this bond atpriceP would have an IRR of y. However, the quoted yield on this bond in order to produce anIRR of y must be higher thany because of the effect of taxes. An investor buying this bond atP would be quoted a tax-exempt yieldy that satises the equation:

P =N

n =1

100 × C/ 2(1 + y/ 2)n +

100(1 + y/ 2)N .

For a bond wherey ≤ C , the bond price is greater than 100 and there are no tax effects(τ = 0 ) and y = y. For bonds wherey > C , the tax reduces the nal bond payment andlowers the bond price, consequently raising the tax-exempt yield,y, on these bonds relative to

18



the municipal yieldy. Thus, we can compute the additional yield required by bonds subject totax, y − y, for these bonds to have the same required return as a newly issued municipal securitywith yieldy. The yield difference,y − y, is the additional yield that a municipal bond subjectto tax would need to bear in order for an investor buying that bond to have an IRR of y.

To illustrate the effects of taxes, we chooseC = 2 .35%, which is the median coupon rate inthe sample (see Table 1). In Figure 5, we graph the additional yieldy − y required by this bondto produce an IRR of y, which is the yield on fully non-taxable municipal bonds. We graphy onthex-axis andy − y in basis points on they-axis. We also conservatively assume thatτ I = 0 .35

andτ C = 0 .15, the lowest tax rates in our sample. These are conservative choices because taxeffects will be larger as the tax rates are higher in the early years of our sample. We considerthe case for maturities of 2, 5, and 10 years. Naturally, as maturity shortens, the effect of taxesrises because the nal tax payment at maturity is worth more in present value terms. We varyy from zero to 6%. The effect of taxes increases withy as there is a larger tax payment on thecapital gain when the purchase price of the bond decreases asy increases.

Figure 5 shows that the effect of taxes should not be negligible and cannot be easily ignored.Belowy = 2 .35%, there are no tax effects, soy − y = 0 . As the yield rises above 2.35%, theprice of the bond falls below par and the bond rst becomes subject to capital gains taxes. Thiseffect is fairly small, at around 5 basis points. Asy further increases, income taxes now applyand there is a discrete jump iny − y. Fory = 0 .03, the additional yield required is already

around 20 basis points, even for a 10-year maturity. We should expect to see effects of at leastthis magnitude in data. As yields reach 6%, the additional yields required are over 100 basispoints for a 10-year bond, but this is an extreme case.

In summary, if taxes are important determinants in municipal bond prices, we should expectto see non-zero differences in cross-sectional yields for bonds with low prices, relative to theirtaxable boundaries. We now examine just how large the tax premium is in data.

4.2 Tax Effects in the Cross Section

To characterize the effects of taxes on the cross-section of municipal bonds, we partition alltrades into one of seven bins based on the transaction priceP based on their tax treatment:

19



Transaction Price Bins Tax Treatment

1 P > RP + 1 .0 No Tax2 RP + 0 .5 < P ≤ RP + 1 .0 No Tax3 RP ≤ P ≤ RP + 0 .5 No Tax4 DM < P < RP Capital Gains Tax5 DM − 0.5 < P ≤ DM Income Tax6 DM − 1.0 < P ≤ DM − 0.5 Income Tax7 P ≤ DM − 1.0 Income Tax

The rst three bins lie in the no-tax region and the middle bin (DM < P < RP ) containsbonds subject to capital gains taxes at redemption. The last three bins comprise bonds whichtrade below the de minimis boundary and are subject to income tax. Note that the revisedprice and de minimis boundary are unique to each bond and change over time. We dene theboundaries of these bins based on bond prices because the IRC denes the tax regions in termsof bond prices.

To understand these partitions, consider the case of a par bond, where the revised price is parvalue. The rst three bins contain transactions where prices are above $100 par value: pricesgreater than $101, prices between $100.50 and $100, and prices between $100 and $100.50.If a par bond trades below $100, it is subject to tax. In the middle bin containing transactionsabove de minimis to $100, an investor must pay capital gains tax. The last three bins contain

transactions of below de minimis bonds, where income tax rates apply. These bins are speciedin relative terms from the de minimis boundary: from 50c below de minimis to de minimis, from$1 below de minimis to 50c below de minimis, and trades more than $1 below de minimis. Foran OID bond, revised price and the de minimis boundary depend on the OID accretion schedule,and the bins change boundaries appropriately.

Yield Differences Across Bonds

Figure 6 reports the averages of transactions yields across the bins (“Yield”). For each trans-action on each trading day, we also compute the theoretical prices of bonds from that day’szero-coupon yield curve and also the implied yield from the model price, which we refer to as“Model Yields” following equation (5). These model yields take as given the zero curve and donot account for tax effects. The dotted lines in each panel represent 95% condence intervals.These condence bands are very tight, on average around 4 basis points. In the top panel of Figure 6, we compute the averages using all trades. The other panels use only ask prices, bid

20



prices, and interdealer trades, respectively.Figure 6 shows that the model-implied yields are fairly at across the buckets. This is as

expected because if the zero yield curve does represent fundamental value and there are no taxeffects, the model-implied yields should be perfectly horizonal if each bin contains bonds of the same maturity. There is an approximately 20 basis point increase in model-implied yieldsfor bonds trading between revised price and de minimis (DM < P < RP ) compared to theadjoining bins for the model-implied yields. This is because the average maturity of trades inthis bin is slightly higher, at 5.68 years, compared to the no-tax and income tax regions withaverage maturities of 4.60 and 4.53 years, respectively.

In sharp contrast to the fairlyat model-implied yields, theactual tax-exempt yields increasedramatically as we move from the no-tax region to the income tax region. In the top panel usingall transactions, the average yield of bonds whereP > RP + 1 .0 is 4.00%. As bonds crossinto the capital gains region,DM < P < RP , yields increase to 4.23%. For deep below deminimis bonds whereP ≤ DM − 1.0, average yields are 4.78%, which is 78 basis points higherthan the bonds with the highest prices. Taxes seem to matter for municipal bond prices! This isconsistent with other papers documenting that individual investors react rationally to tax effectsin other asset pricing decisions, like allocations to mutual funds or tax-deferred accounts (see,for example, Bergstresser and Poterba, 2002; Bernheim, 2002). Our results show that taxesaffect even the relative prices of tax-exempt bonds.

These patterns are repeated taking only transactions at the ask and at the bid in the middletwo panels, which also illustrate the large bid-ask spreads in the municipal bond market. Forask transactions, the average yield line now lies lower than the model-implied yields. The askyields start at 3.66% for theP > RP + 1 .0 bin and rise to 4.25% for the lastP ≤ DM − 1.0

bin, so there is an increase of 59 basis points going from the rst bin to the last bin. For bidtransactions, the actual yields always lie on top of the yields implied by the zero-coupon yieldcurve and monotonically increase from 3.91% for bonds with the highest prices to 4.69% fordeep below de minimis bonds. Finally, the last panel of Figure 6 shows that for interdealertrades, the yield difference between bins 1 and 7 is 43 basis points.

Benchmarking to the Zero Curve

We take a closer look at the yield spreads across premium and discount bonds in Table 3, whichreports the transaction yields relative to the model-implied yields. Panel A reports the averageyield spread for different types of trades, where the yield spread is dened as the transaction

21



yield minus the zero-implied yield. Panel A reports the same information as Figure 6, exceptwe report more detailed information for the yield spreads.

In computing averages of the yield spreads, we take days where at least one trade takesplace in all the bins. Table 3 reports the number of days used in the computation and theaverage number of bonds in each bin. For all trades, we compute averages across 2,101 tradingdays, and on a given trading day, the average number of trades in each bin ranges from 32 to1,528. The number of trading days is smallest taking only ask trades, at 989, but in across alltypes of trades, there are at least 13 observations per trading day in each bin. We report standarderrors in parentheses. Not surprisingly, these standard errors are very small because of the verylarge number of observations.

Panel A shows that for all trades, the average yield spreads in the rst three no-tax binsare less than 4 basis points. There is little effect of a bond trading in the capital gains taxregion, with a yield spread in theDM < P < RP bin of 4 basis points. However, oncebond prices decline below de minimis, there are increasingly large spreads. Bonds trading upto $0.50 below de minimis have yields 27 basis points higher than what the zero curve predicts.Bonds with prices $1.00 or more below de minimis have yields 62 basis points higher than themodel-implied yields.

Panel A also reports that these patterns are robust to considering other transactions types.For example, ask transactions trade approximately 16-18 basis points below the municipal curve

for bonds above the de minimis boundary, and up to 21 basis points above the curve for deepbelow de minimis bonds. Interdealer trades are 1-2 basis points above the municipal zero curvefor above de minimis bonds and trade up to 44 basis points above the zero curve for bondstrading below de minimis. These are economically very large differences in yields.

Our economic analysis suggests that the results in Panel A should not be surprising: taxesshould theoretically affect the cross-sectional pricing of tax-exempt bonds and the data showthat this is the case. We now turn to the question of whether the higher yields earned by munic-ipal bond subject to tax are fair compensation for bearing that tax. If investors buying taxablemunicipal bonds correctly anticipate that they must pay tax and assume that the tax paymentsoccur at maturity, then investors buying below de minimis bonds will be receiving the after-tax yield in equation (2). We dene the after-tax yield spread as the transaction after-tax yieldminus the model-implied yield. We report these spreads in Panel B of Table 3.

Not surprisingly, Panel B shows that the after-tax yield spreads are smaller than the raw yieldspreads in Panel A. However, they are not zero, as would be the case if equation (2) perfectly

22



accounted for tax effects. Note that the after-tax yield spreads are exactly the same as the tax-exempt yield spreads in Panel A for the rst three price bins in the no-tax region as by denitionthere are no tax effects. For all trades, bonds in the capital gains region,DM < P < RP , arepriced almost at fair value. However, as bonds enter below de minimis territory, the yieldsof below de minimis bonds are higher than what equation (2) predicts. Specically, for bondstrading more than $1.00 below de minimis, an investor could make an after-tax prot of 28 basispoints per annum relative to the zero curve, by buying these bonds, holding them to maturity,and paying the tax on market discount.

Panel B shows that there is much less of a difference between deep below de minimis bonds(bin 7) and bonds with high prices (bin 1) for ask trades, with a difference of only 7 basispoints. For bid and interdealer trades, there are differences of 27 and 10 basis points betweenbins 1 and 7. Thus, dealers are potentially earning a large proportion of the extra yield notdirectly explained by the zero curve in purchasing below de minimis bonds from customers.Retail customers or buy-side institutional investors would be much better off holding bondswith market discount to maturity than by selling them.

4.3 Empirical Duration, Default Risk, and Trade Size

In Table 3, the positive after-tax yield spreads indicate that investors are demanding more com-pensation for bearing municipal bonds subject to tax than can be explained by simple discount-ing of after-tax cashows using the zero curve. This taxation premium may be due to theparticular characteristics of bonds such as empirical duration, default risk or trade size, whichwe now investigate.

Empirical Duration

Besides yield or price levels, municipal bond traders often consider duration risk in the manage-ment of their portfolios. The higher yields on below de minimis bonds may represent compen-

sation for bearing bonds with duration that is not captured by the zero curve. Managing theseduration exposures may be important for tracking, or benchmarking, against index positions.

In Table 4, we compare empirical duration with model-implied durations. We compute theempirical duration for a bond if the previous trade of the bond occurs within the past 30 daysand the price level of the last trade occurs in the same tax region as the current trade. Bins 1-3represent the no-tax region, bin 4 is the capital gains tax region, and bins 5-7 are the income tax

23



regions. The empirical duration is computed as

D t =(P t − P last )/P last

Y t − Y last, (8)

whereP t is the current trade price of the bond with tax-exempt yieldY t andP last is the price of

the bond within the last 30 days with tax-exempt yieldY last . Similarly, we compute a model-implied duration:

D mt =

(P mt − P mlast )/P mlast

Y mt − Y mlast, (9)

which instead uses the bond prices and tax-exempt yields implied by the zero coupon yieldcurve. We report the empirical and model duration for each of the seven price bins. We areparticularly interested in the duration spreadD − D m , which is the empirical duration notcaptured by the theoretical zero curve.

Table 4 reports that duration in excess of the zero curve is larger for bonds well in the no-tax region than for deep below de minimis bonds. For bin 1 with prices greater than $1.00above revised price,D − D m is 2.12, whereas bonds in bin 7 trading at least $1.00 below deminimis have a duration spread of 1.62. These patterns are also observed when only interdealertrades are considered, where bonds in bins 1 and 7 have almost the same duration spreads, withD − D m being 1.86 and 1.70, respectively. Thus, the higher yields for below de minimis bondsis not due to these bonds having higher empirical duration than the zero curve implies comparedto municipal bonds without market discount.

Controlling for Default Risk

Investors may demand an after-tax premium to hold below de minimis bonds because theyfear these bonds may carry higher default risk than a typical A-grade municipal security. Werst consider only short maturity bonds with maturities between 1-2 years where cumulativedefault risk is smallest. Investors with shorter horizons who cannot hold bonds for long periodswould also focus on these maturities. Panel A of Table 5 reports that for bonds with 1-2 year

maturities, the difference in the after-tax yield spread between bonds with prices greater $1.00above revised price (bin 1) and deep below de minimis bonds trading at prices lower than $1.00below de minimis (bin 7) is over 72 basis points, with after-tax yield spreads of -8 basis pointsand 63 basis points, respectively in bins 1 and 7. This after-tax yield spread is much largerthan the after-tax yield spread on all bonds of 31 basis points reported in Table 3. The highafter-tax yield spreads on short maturity bonds are especially puzzling because these bonds aremost likely to be held to maturity and the investments carry little cumulative default risk.

24



By construction, our sample is specically constructed to minimize default risk by takingonly A-grade bonds. Nevertheless, as a second default risk control, we take only insured bondswith the highest AAA credit ratings. Panel B of Table 5 reports the after-tax yield spreadson these bonds. The after-tax yield spread difference between bins 1 and 7 is 21 basis points,indicating that insurance per se does not remove the de minimis premium.

The fact that we still observe high yields on bonds with market discount among insuredbonds does not rule out a default story if default is a Peso-event and the bond market is pricingin an extremely rare event. To implement a very strict default control, we employ the followingstrategy. Municipal bonds are usually issued in series, with many bonds of different types andmaturities being issued simultaneously by the same issuer. We consider above and below deminimis bonds with different tax treatments in the same series.

In Panel C of Table 5, we divide bonds from the same series into three bins: aboveRP subject to no tax, betweenRP andDM , and belowDM . Table 5 shows that the yield differenceson bonds with and without market discount are extremely unlikely to be due to default risk.Bonds in the same series with different tax treatments have an after-tax yield spread differenceof 29 basis points between bonds aboveRP and bonds belowDM . This is almost exactly thesame as the spread of 31 basis points among all bonds reported in Table 3.

Controlling for Liquidity

We consider three controls for liquidity. First, we take only New York and California bonds inPanel A of Table 6. These issues are generally more liquid than other states and comprise 26.5%of all trades (see Table 1). Panel A nds that for these states, the after-tax yield spread for bin7 is smaller, at 12 basis points, compared to 28 basis points for all states in Table 3. However,even in these markets, the high yields of below de minimis bonds persist, with a difference of 18 basis points between the after-tax yield spreads of bins 1 and 7.

Second, the high spreads on municipal bonds with market discount may vary as the propor-tion of below de minimis trades varies. Specically, the path of municipal interest rates in thebottom plot of Figure 3 shows that 5-year interest rates rose from 4 to 5% over 1999 to 2000 andthere were a large proportion of trades that involved below de minimis bonds in 2000. There arealso large numbers of below de minimis trades in 1995. In Panel B, we remove trades in 1995,1999, and 2000. Excluding this subsample, we observe slightly larger after-tax yield spreads of 37 basis points for bin 7 excluding the 1995, and 1999-2000 subsample, compared to 31 basispoints in the full sample (see Table 3). A larger proportion of below de minimis trades only

25



seems to be weakly related to the high yields on below de minimis bonds.As a nal liquidity control, we match trades by transaction size. For each trade in the price

bin with prices more than $1.00 below de minimis (bin 7), we match trades in bin 7 with a tradeof exactly the same par amount traded among bonds trading at least $1.00 above their revisedprices (bin 1). If no matching trade is found in bin 1, we do not consider that transaction. If there is more than one trade in bin 1 with the same par value traded as the trade in bin 7, wetake a random trade of the same transaction size. Panel C shows that controlling for transactionsize slightly reduces, but does not change our results. The difference in after-tax yield spreadsof 26 basis between bins 1 and 7 is only slightly smaller than the raw 31 basis point spread,without matching for transaction size, in Table 3. In summary, controlling for liquidity slightlylowers the high after-tax yields on tax-exempt bonds subject to market discount tax, but doesnot eliminate them.

4.4 Characterizing the De Minimis Premium

To further characterize the de minimis premium, we perform a cross-sectional regression inTable 7. We take the spread of actual after-tax transaction yields less model-implied yields,measured in basis points, for bonds trading below de minimis. We regress the after-tax yieldspread onto various independent variables. We investigate the effects of par value, maturity, thedistance to the de minimis boundary, and issue price. We measure the distance to de minimisas DM − P in dollars per $100 par value. We report selected coefcients on xed effects, butalso include time dummies for each year and for the eight largest states in terms of transactionvolume (CA, NY, FL, TX, NJ, MI, OH, and PA).

To establish a base case, consider an original general obligation par bond issued in NYcarrying an AAA rating which is insured. This bond sells in an interdealer below de minimistrade with a trade size of $50,000 and has a 5-year maturity at the time of trade. (Table 1 reportsthat $50,000 is the median trade size in our sample.) Suppose that this bond trades at $0.50

below par. The after-tax yield spread on this trade, from the estimated coefcients in Table 7 is34 basis points in 2005. That is, an investor buying this bond would receive an extra 34 basispoints in yield after tax by buying this bond compared to what the zero yield curve warrants.

Table 7 reports that below de minimis bonds with larger trade sizes have lower yield spreads.If the trade size increased to $1 million, the after-tax yield spread would decline, on average,by 10 basis points. This is consistent with our relatively weak effect our liquidity controls

26



produced in Table 6. If this bond instead carried a 1-year maturity, the after-tax yield spreadwould widen to 42 basis points. Decreasing the bond price from $0.50 below par to $1.50below par would increase the after-tax yield spread to 35 basis points compared to 34 basispoints. Hence, controlling for everything else, it is not so much the distance to de minimis butthat the bond is trading below de minimis that causes its high after-tax yield spread. From thecoefcients in Table 7, the original issue price of the bond has the weakest effect, implying thatthere is little economic effect of the bond’s original issue price on the after-tax yield spread.

We also report the coefcients on selected xed effects in Table 7. While these are highlystatistically signicant because of the large number of observations, the economic effects of whether the bond is a general obligation bond or revenue bond is minimal. There is also only asmall effect if this bond moved from being AAA and becomes an AA bond, with the after-taxyield spread increasing from 34 to 37 basis points.

4.5 Events When Bonds Cross Taxable Regions

In this section, we track individual bonds as they cross into or out of each of the taxable regions.This event-study approach is useful because it gauges the effects of tax on thesame bond, ratherthan considering the prices of different bonds in the cross section. We examine all events whentheRP or DM boundaries are crossed over short periods.

Crossing the RP Boundary

In Table 8, we examine the crossover events between the no-tax region and the capital gains taxregion. The boundary between these regions is the revised issue price,RP . We trace throughthe effects of bonds crossing down throughRP and up throughRP . We only consider bondsentering or leaving the capital gains tax region to the no-tax region, with no below de minimistrades counted. We dene the rst trade crossingRP as event time zero. We rst consider thesecrosses using all transactions in Panel A. In the rst two rows, “Crossing Down” and “Crossing

Up,” we track trades whose last trade prior to the cross occurred within the last ve tradingdays, but not on the same trading day, as the event trade. In the last two rows, “Crossing Downon the Same Day,” and “Crossing Up on the Same Day,” we consider trades where the last tradeprior to the cross and the trade crossingRP occur on the same trading day.

Not surprisingly, Panel A shows that yields of bonds entering (leaving) the capital gains taxregion increase (decrease). Bonds becoming subject to capital gains tax see their yields increaseby 27 basis points if the last trade occurs up to 5 days prior, and 21 basis points if RP is crossed

27



on the same day as the last trade. As bonds leave the capital gains region, their yields decreaseby 37 basis points compared to their last trade up to 5 days ago, and bonds which cross upthroughRP on the same day as the last trade decrease their yields by 25 basis points. Thetheoretical changes in these yields, reported in the second last column labeled “∆ Y m0 ” for fullytax-exempt bonds are two orders of magnitude smaller than the reactions we see in data.

In the column labeled “∆ Y 0 ,τ ,” we report the changes in the after-tax yields between the lasttrade and the event trade. If we fully account for tax effects using the present value model inequation (2), then these changes in after-tax yields should be close to the changes of the model-implied yields. The changes in after-tax yields are smaller than the changes in tax-exemptyields, but the differences are minimal, at well below 1 basis point. Thus, agents seem to bedemanding larger yields than what the tax effects warrant and give up too much yield when thetax effects are removed.

In Panels B-D, we consider ask, bid, and interdealer trades, respectively. In Panel B (C),we take trades where both the trade prior to the event and the event trade crossingRP bothoccur at the bid (ask), while in Panel D, both the last trade and event trade must be interdealertransactions. In all cases, we nd that the actual changes in yield in data are two orders of magnitude larger than the changes implied by the zero-coupon curve. For interdealer trades,bonds which cross up throughRP when the last trade occurred up to 5 days ago decrease theiryields by 20 basis points, compared to the model-implied yield change of around 1 basis point.

As the change in the after-tax yields is -18 basis points, only 2 basis points of the 20 basis pointdecrease can be traced to tax effects using equation (2).

Crossing the DM Boundary

Table 9 examines bonds crossing over the de minimis boundary. These are bonds which crossfrom the income tax region, but as they cross they may enter either the capital gains tax region,DM < P < RP , or the no-tax region,P ≥ RP . Similarly, we track bonds trading above deminimis, which could be either fully tax-free or subject to capital gains tax, and then becomesubject to income tax. We dene the rst trade crossingDM as the event trade. Panel Aconsiders all such trades, while we consider trades where the event trade and the prior trade areboth bid, ask, or interdealer trades in Panels B-D, respectively.

Panel A shows that bonds entering the below de minimis region increase their yields by 57basis points when their last trade occurred up to 5 days prior. The model-implied yield changeis less than 1 basis point. The change in after-tax yields is 39 basis points, so taxes should only

28



account for 18 basis points of the 57 basis point change. Investors seem to be demanding anextra 39 basis points to hold bond subject to income tax. For bonds crossingDM on the sametrading day, the increase in after-tax yields is 27 basis points. Similarly, as bonds crossDM

to lower tax regions, the decrease in after-tax yields is 44 basis points for bonds where the lastand event trade are not on the same day. Thus, investors willingly give up 44 basis points to notsubject themselves to income tax.

The change in after-tax yields crossing theDM threshold are still large for ask and bidtrades in Panels B and C. The smallest after-tax yield change, in absolute magnitude, occursfor ask trades for bonds crossing into the belowDM region on the same day. In this case, theafter-tax yield increases by 15 basis points. In Panel D, the change in after-tax yields of bondscrossingDM for interdealer trades remains over 17 basis points in absolute magnitude for alltrades crossing the de minimis boundary. These are approximately the same as the around 14basis point changes for bonds involving interdealer trades crossing theRP boundary in Table 8.

In summary, bonds crossing into taxable thresholds suddenly trade at higher after-tax yieldsthan what taxes seem to justify. Similarly, investors seem to be willing to give up after-tax yieldswhen bonds cross in regions with lower tax treatments. We now turn to estimating exactly whattax rates are priced by individual investors when the de minimis boundary is crossed.

4.6 Implied Tax Rates

As bonds cross the de minimis boundary downward from the capital gains or no tax regions,bonds suddenly become subject to income tax. We use the rst trade below de minimis to inferthe new estimated income tax rate faced by an investor, assuming the bond is held to maturity.This trade is especially important because it is the rst observation where investors are reactingto a new tax treatment. Similarly, as bonds enter the capital gains region from the below deminimis region, their tax burdens are lowered and we can estimate the implied capital gainsrate from the rst trade in the capital gains region. In particular, we take all the events where

the last trade before the cross happens within ve days, including last trades on the event day.These implied tax rates shed light on how much yield investors are giving up or demanding astax liabilities lessen or increase.

The Implied Income Tax Rate

To estimate the implied income tax rate, we consider events where bond prices go down throughthe de minimis boundary. The rst trade in the below de minimis region has a price of P . The

29



market discount on this is taxed at regular income tax rates if the bond is held to maturity. If P m denotes the model-implied price if the bond were not subject to tax, the difference betweenP andP m is the present value of the tax liability:

P = P m −(RP − P ) × τ I

(1 + r N / 2)N − 1+ w(10)

whereτ I is theestimated income tax rate. This is a very simple expression because all municipalbond coupons are tax exempt. To estimateτ I , we put a rational expectations error on the RHSof equation (10). This is just an OLS regression to which we add xed year effects and othercontrols.

Panel A of Table 10 reports the estimated implied income tax rates. Using all prices, theimplied income tax rates that will equate the actual price and the price implied by the zerocurve is 79%. We also consider the effect of only ask (bid) trades, where the last trade within

the previous ve days is also an ask (bid). If we take only these ask trades or bid trades,the estimated income tax rates are 73% and 120%, respectively. The implied tax rate fromconsidering only interdealer trades, with the prior trade also being an interdealer trade, is evenlarger than using all trades, at 101%. These income tax rates are signicantly higher than thehighest marginal income tax rate in our sample, at 39.6%. Certainly, the initial jump downwardsfor bonds rst trading in the below de minimis region are larger than what any reasonable taxrates warrant.

We also estimate implied income tax rates in each year. These are always much higher thanthe statutory income tax rates (which are a maximum of 39.6% in our sample), except during2002. While the rst trades of bonds entering the below de minimis area are generally at adiscount (under-priced) compared to the zero curve, this was not the case in 2002. We estimatean implied income tax rate of 7.4% in 2002, with a standard error of 13.4%. This coincideswith a drop in the statutory tax rates from 38.6% in 2002 to 35% in 2003. During the early2000’s, the Economic Growth and Tax Relief Reconciliation Act of 2001 progressively reducedincome tax rates from 39.6% in 2000, but The Jobs and Growth Tax Relief Reconciliation Act

of 2003 accelerated these and reduced the income tax rate to its present level of 0.35 from 2003onwards. Our estimated income tax rate shoots up to 163% in 2003, with a standard error of 8.6%.

The Implied Capital Gains Tax Rate

To estimate implied capital gains tax rates, we take all events where bonds cross upwards acrossthe de minimis boundary and fall into the capital gains tax region (fromRP to DM ). Bonds

30



making this transition go from being subject to income tax to being subject only to capital gainstax. To estimate the implied capital gains tax rate, we use the equation:

P = P m −(RP − P ) × τ C

(1 + r N / 2)N − 1+ w , (11)

where the difference between the actual priceP and the model-implied priceP m

is the presentvalue of the tax liability payable at maturity, which is taxed as a capital gain. We estimateτ C inequation (11) by using an OLS regression with year and other dummies.

Panel B of Table 10 shows that for all trades, the estimated capital gains rate is slightlybelow zero, at -4%. For ask and bid trades, the implied capital gains rates are 1% and 20%, re-spectively. The implied capital gains rate is negative taking only interdealer trades, at -9%. Theimplied negative tax rates indicate that prices are moving upward from the below de minimisregion into the capital gains region as if the federal government is paying investors to hold thesebonds. Alternatively, investors are paying a premium to enjoy relief from the previous incometax regime.

5 Conclusion

Municipal bond markets are a unique place to study the effects of individual tax rates becauseindividuals are likely to be the marginal pricers in this market. We nd that taxation plays an

important role in determining municipal bond prices. Although coupon payments and originalissue discount of municipal bonds are exempt from federal income tax, the prots of tradingmunicipal bonds in secondary markets are taxed at capital gains or income tax rates. The num-ber of municipal bonds subject to tax is not small; in some years the proportion of municipalbonds transactions subject to income tax on market discount is above 30%. Furthermore, the taxcode mandates discontinuities in the tax treatments of bonds. As the price of a bond originallyissued at par falls below par, it rst becomes subject to capital gains tax rates. As it falls further

in price, it becomes subject to income tax. The boundary between the capital gains and incometax regions is called the de minimis boundary.We show that the additional yield on municipal bonds carrying income tax liabilities that is

required for these bonds to have the same IRR on an after-tax basis as a fully non-taxable mu-nicipal bond is theoretically not negligible. Consistent with this, we nd that in data, municipalbonds with income tax liabilities carry higher yields than municipal bonds not subject to marketdiscount taxation. Bonds trading deep below the de minimis threshold have the highest tax lia-

31



bilities and these bonds have the highest yields. These effects are both highly statistically andeconomically signicant. Thus, taxes matter for the relative pricing of tax-exempt securities.

However, we nd that the yields on municipal bonds subject to tax are higher than what canbe explained by valuing the after-tax cashows of the bond using the zero-coupon municipalyield curve. In particular, municipal bonds in A-grade credit classes bearing the highest taxburdens have after-tax yields approximately 30 basis points higher than the tax-exempt yieldcurve. The high after-tax yields on municipal bonds with market discount persist when wecontrol for default risk and liquidity. The income tax rate implied by transaction prices of bonds rst entering the income tax region is around 80%. These results suggest that taxes playan important role in pricing municipal securities, but the effect of taxes is larger than whatstandard discounting models can capture.

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Appendix

A Taxation of Market Discount for Bonds Sold Prior to Ma-turity

The general principle involved in the taxation of market discount for bonds not held to maturityis that there is a second accretion schedule that applies to the purchase price of the bond, whichis computed using the yield at the time of purchase. Any resulting capital gain or loss is com-puted relative to this second accrual of discount, sometimes termed total discount. It is best toillustrate this concept with a few examples. We rst consider the case of original issue premiumand par bonds, followed by OID bonds.

A.1 Premium and Par Bonds

Tax Treatment

Consider a bond with an original 10-year maturity with a 10% coupon. We refer to this bondas Bond A. Suppose that two years after issue att = 2 , Bond A trades at a price of $95. Themarket discount on this bond at the time of purchase is100− 95 = $5. Suppose that att = 8 , thebond is sold for $99. Thus, fromt = 2 to t = 8 , the investor has made a gain of 99 − 95 = $4.A portion of this $4 gain is taxed as ordinary income and a portion is taxed as a capital gain.

When Bond A is purchased att = 2 for $95, the investor purchasing Bond A does so ata yield of 10.9543%. As Bond A approaches maturity, the price of Bond A would determin-istically approach 100 under the constant yield method if the yield was constant at 10.9543%.This accretion of discount is taxed as income under IRC § 1276. Anything in excess of thisaccretion is dened as a capital gain. Att = 8 , the revised price of Bond A, computed as thepresent value of the remaining four 5% coupons at a yield of 10.9543%/ 2 = 5.4772% every sixmonths is $98.3266. The accretion of market discount of 98.3266 − 95 = $3.3266 is counted

as income. Thus,4 − 3.3266 = $0.6734 is taxed as income.We illustrate this in the top panel of Figure A-1. The accretion of market discount at the

purchase yield of 10.9543% is shown in the dashed red line. This accretion is taxed as income.At t = 8 , the difference between the sale price of $99, denoted as the red square, and theaccreted purchase price of Bond A of $98.3266 is $0.6734 and it is taxed as a capital gain.

The accretion of market discount affects the tax basis of the bond. Any sale of Bond Abelow the accreted market discount can be deducted as a loss. This also applies to purchases

33



at a premium. While the amortization of municipal bond premiums as a result of secondarymarket transactions cannot be deducted, the amortization of the premium changes the tax basisof the bond.

Figure A-1 also shows the de minimis boundary. Any purchase above the de minimis thresh-old results in no market discount. Att = 2 , Bond A’s de minimis boundary is100(1− 0.0025×

8) = $98. Suppose that att = 2 , Bond A is purchased for $98.50 and sold att = 8 for $99.Then, the99 − 98.50 = $0.50 prot is taxed entirely as a capital gain.

Ex-Ante Incentive to Sell Later

If the yield on the purchased bond remains constant aty, then a par or premium bond purchasedin the secondary market would never be sold early. In this environment, a par or premium bond’svalue would rise in accordance with the revised price schedule, which changes according to

P n = P n − 1 (1 + y/ 2) − 100 × C/ 2,

in each subsequent 6-month period, withP 1 being the clean purchase price. For a par or pre-mium bond,y > C and the revised purchase price accelerates as the bond approaches maturity.Taxes are not paid each period onP n − P n − 1 , which would be the timing appropriate if taxesare levied when the economic income is earned. Instead, taxes are levied onP n − P 1 only atthe time of sale. Not surprisingly, it is straightforward to show that pushing out the paymentof the tax increases the after-tax value of the cashows valued aty, and thus the after-tax yieldincreases as the sale is deferred.

The value to waiting is economically very small. For example, suppose that the income taxrate is 35%. If a par bond with an initial coupon of C = 1% and a remaining 30-year maturityis purchased at a tax-exempt yield of 20%, then the after-tax yield if the bond is sold after 6months is 19.9771%, compared to 19.9773% if the bond is held to maturity, assuming in bothcases that the yield curve remains at aty. Higher tax rates, shorter maturities, or lower couponrates (initial yields) will cause these differences to be even smaller.

There is one counter-argument for an investor to sell a par or premium bond early. Inupward-sloping yield curve environments, which has always been the case in the municipalmarket, Bankman and Klein (1989) show that the constant yield accrual method understatesinterest income in the early years and there is too much accrual in later years. If yields are heldconstant, selling early would result in a lower tax payment. However, Sims (1992) numericallyshows that such effects are very small, but they would off-set the incentive for investors to notsell early to defer tax.

34



A.2 OID Bonds

Tax Treatment

The taxation of market discount for OID bonds depends on the OID accrual schedule relativeto the accrual schedule for the market discount. This is best illustrated through an example.Consider Bond B, which is an OID bond originally issued with a 10-year maturity paying a10% coupon. Bond B was issued at a price of $88.5301 with a par value of 100 with an initialyield of 12%. Suppose that at timet = 2 , Bond B is purchased for $84, corresponding to ayield of 13.3105%, and att = 8 , Bond B is sold for $99. The computation of taxable marketdiscount is complicated by the fact that the accreted OID is not taxable.

The bottom plot of Figure A-1 illustrates this case. The solid blue line plots the accretionof OID at the original issue yield of 12%. These are the revised prices of Bond B according to

the OID accrual schedule. Att = 2 , the purchase price is denoted by a red diamond, and thispurchase price is accreted at the purchase yield of 13.3105% in the dashed red line. In FigureA-1, the vertical line att = 2 is the difference between the purchase price of $84 and the revisedprice of $89.8941.

At t = 8 , Bond B is sold for $99, which we denote on Figure A-1 by the red square.Normally, the accretion of the purchase price fromt = 2 to t = 8 along the dashed red curvewould be subject to income tax. However, some of this accretion is exempt from tax because

accretion would have happened under the OID accrual schedule. It is only the accretion of themarket discount in excess of the OID accretion that is taxable.

Fromt = 2 to t = 8 , the revised price of Bond B under the OID schedule increases from$89.8941 to $96.5349. The OID accrual schedule can be computed by valuing the remainingpayments of Bond B at the original issue yield of 12%. This difference in OID of 89.8941 −

96.5349 = $6.6408 is not taxable. When Bond B is purchased att = 2 , we apply the constantaccrual yield method to compute the accrual of total discount at the purchase yield of 13.3105%.At t = 8 , we can compute this accreted discount by valuing the remaining four payments of $5every six months plus the nal par value of $100 at a yield of 6.6553% every six months, whichtotals $94.3495. According to the total discount schedule, there is an increase of 94.3495− 84 =

$10.3495. However, according to the OID schedule, we would originally have seen an increasein the bond price of $6.6408. The taxable market discount is the difference in the accrued OIDand the total discount accrual, so only10.3495 − 6.6408 = $3.7087 is subject to income tax.

In Figure A-1, the difference between the two vertical lines represents the accrued market

35



discount at the time of sale. The vertical line att = 2 is the market discount at purchase, whichis 89.8941 − 84 = $5.8941. The vertical line att = 8 is the market discount at sale, which is96.5349 − 94.3495 = $2.1854. The difference between these two vertical lines is the accruedmarket discount, which is5.8941 − 2.1854 = $3.7087. According to IRC § 1276(a)(1), onlythis portion of the total gain is treated as ordinary income.

To summarize, the total gain involved in purchasing Bond B att = 2 for $84 and sellingBond B att = 8 for $99 is $15. The OID accrual fromt = 2 to t = 8 of $6.6408 is not taxable.Thus, the total taxable income is99 − 84 − 6.6408 = $8.3592 at the time of sale. Att = 8 , theinvestor owes income tax on $3.7087 and the remainder of $4.6505 is taxed as a capital gain.

For a second case, suppose that att = 2 , Bond B is trading for $89, which is above the deminimis boundary of Bond B att = 2 , which isDM = 89 .8941− 100× 0.0025× 8 = $87.8941.Bond B is sold att = 8 for $99. Bond B is not subject to market discount as the purchaseprice is above the de minimis threshold, but below the revised price of $89.8941 att = 2 .Thus, no income tax is payable but some of the99 − 89 = $10 gain is taxable as a capitalgain. According to the OID schedule, $6.6408 is not taxable, so the total taxable income is99 − 89 − 6.6408 = $3.3592, which is taxed at the capital gains rate.

As a nal case, suppose that att = 2 , Bond B trades above its accreted OID schedule for$91. Again suppose that Bond B is sold att = 8 for $99. In this case, no income tax on the gainis paid and since some of the OID accretion is tax-free, not all of the99 − 91 = $8 is taxed.

Fromt = 2 to t = 8 , the change in the OID schedule is $6.6408, so the total taxable income is99 − 91 − 6.6408 = $1.3592 on which capital gains tax is owed.

Ex-Ante Incentive to Sell Early

With OID bonds, there is a difference between the OID accrual and the purchase price accrual.Because the purchase yield is larger than the initial yield, the accrual of the total discount on thepurchase price is faster than the accrual of OID. Since OID is tax-exempt, there is an incentiveto bring forward the sale of the bond. This does not occur for a par or premium bond becausethe revised price is always xed at par value.

For realistic cases, the additional advantage of selling early is worth less than 1 basis point.Consider an OID bond with original coupon rate 2.35% (the median coupon in Table 1) withan original issue yield of 5% and a remaining maturity of 10 years. We assume the tax-exemptyield curve is at at 6% and remains constant. If the income tax rate is 0.396, then the after-taxyield assuming a sale in six months is 5.6971% compared to 5.6954% if the investor holds the

36



bond to the full 10-year maturity.

B Data Filters

From January 1995 to November 2005, the original MSRB database contains 58,791,805 indi-

vidual transactionson 1,974,798 unique municipalbonds. Our nal sampleconsists of 5,372,631trades on 259,471 unique securities.

1. Tax Status

We consider only bonds that are exempt from federal and state income taxes. Some tax-exempt municipal bonds issued by state and local governments to nance capital projectsare classied as private activity bonds and are subject to the AMT. These bonds comprise

approximately 3.4% of all CUSIPS and we exclude these bonds from our analysis. Wealso limit our bond universe to bonds issued in one of the 50 states, and so we excludebonds issued in Puerto Rico, the Virgin Islands, other territories of the U.S. such as Amer-ican Samoa, the Canal Zone, and Guam. Bonds issued in these territories constitute lessthan 0.4% of all bonds.

2. High Credit Ratings

To focus only on the tax implications of municipal bond trades, we focus on bonds of the

highest credit classes. We take only bonds rated by S&P in the AAA, AA+, AA, AA-,A+, A, and A- categories. Many A Grade bonds obtain their credit rating because theyare insured by a AAA-rated insurer. Slightly over 60% of all bonds are insured in theMSRB sample.14

3. Straight Bonds

We further limit our sample to include only bonds paying xed coupon rates (94.1% of allbonds in the MSRB sample). We also take only straight bonds with no embedded optionfeatures, so all our bonds are xed maturity paying xed semi-annual coupons. Straightmunicipal bonds constitute 50.4% of all the bond universe and they generally have shortermaturities than bonds with embedded options. The average maturity at issue of straightbonds is 6.31 years while the average maturity at issue of option-embedded bonds is 15.76

14 Nanda and Singh (2004) provide a tax-based rationale of why insurance on municipal bonds is value-enhancing for both insurers and municipal bond investors.

37



years. The exclusion of option-embedded bonds is to facilitate our computation of yield-to-maturity and market discounts. Including bonds with callable or sinking bond featureswould entail numerically intensive option-adjusted spread computations involving bino-mial trees to correctly price the embedded options.

After these rst three requirements, we have transactions on 9,950,226 transactions on464,678 unique municipal bonds.

4. Avoiding Newly Issued Bonds

Green, Hollield and Schürhoff (2006) document signicant underpricing in new mu-nicipal bond issues and interesting patterns in the aftermarket trading of these bonds be-tween informed and uninformed customers. To avoid the effect of newly issued bonds,we exclude all the transactions that happened within 30 days of issuance. Transaction of newly issued bonds constitute about 31% of the 9.9 million transactions, reecting thefact that municipal bonds transactions are concentrated during the period right after is-suance. However, almost all of these transactions are not trades near de minimis becausethere is little movement in the yield curve over a 30 day period. We obtain nearly identicalresults when these trades are included in our sample.

5. Maturities Between One and Ten Years

Transactions involving straight bonds with maturities longer than 10 years are scarce be-cause most bonds with long maturities are issued with callable or sinking fund provisions.We use only transactions with maturity shorter than 10 years in our analysis. We also takebonds only with maturities greater than one year because long-term capital gains rates ap-ply only to securities held longer than one year and there is no market discount for bondswith a maturity less than one year.

6. Removing Very Small Trades and Outliers

To avoid the effect of extremely small trades, we exclude all transactions with par amountstraded less than $10,000. Finally, we take only transactions with prices between $80 and$130, and bonds with coupon rates from 1% to 20%.

38



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40



Table 1: Sample Summary Statistics

Panel A: Summary Statistics on Unique CUSIPs

Largest States of Issue CA NY TX MI FL NJ PA OH10.78 8.92 8.83 5.38 4.94 4.67 4.34 3.59

Issue Price Discount Par Premium30.83 24.43 44.74

GeneralType of Bond Obligation Revenue Other

48.71 44.04 7.25

Credit Rating AAA AA+, AA, AA- A+,A,A-73.28 20.91 5.80

Insurance Yes No72.36 27.64

Panel B: Summary Statistics on Transactions

Largest States of Issues CA NY FL TX NJ MI OH PA13.73 12.81 5.96 5.77 4.46 3.47 3.64 3.64

Issue Price Discount Par Premium35.67 13.38 50.95

GeneralType of Bond Obligation Revenue Other

44.90 49.33 5.77

Credit Rating AAA AA+, AA, AA- A+,A,A-68.84 24.59 6.57

Insurance Yes No63.45 36.55

Inter-Trade Type Ask Bid dealer

43.42 24.46 32.12

Coupon Rate 5% 25% 50% 75% 95%1.5% 2% 2.35% 2.62% 3.35%

Par Amount Traded 5% 25% 50% 75% 95%10,000 25,000 50,000 100,000 1,000,000

Maturity at Trade 1-2 Years 2-5 Years 5-10 Years14.25 41.94 43.82

41



Note to Table 1The table lists summary statistics of the municipal bonds in our sample from the MSRB database where wetake only straight bonds paying xed maturities greater than one year and less than ten years at the time of transaction; bonds with an S&P rating of A- or higher; federal andstate-exempt bonds not subject to theAMT;bonds issued in one of the 50 states; bonds trading at least 30 days after original issuance; and transactions of at least $10,000. There are 259,471 unique CUSIPs in our sample with a total of 5,372,631 transactions fromJanuary 1995 to December 2005. Panel A lists proportions of the 259,471 unique CUSIPs falling into variouscategories, while Panel B lists proportions of the 5,372,631 transactions falling into various categories. Forthe par amount traded, we report the traded par amounts at various percentiles of the distribution.

42



Table 2: Distribution of Original Issue Prices

Issue Price Relative to $100 Par Number Percentage

Original Issue Discount ≤ − 20 103 0.04− 20 < and≤ − 15 47 0.02− 15 < and≤ − 10 57 0.02− 10 < and≤ − 5 304 0.12− 5 < and≤ − 2.50 1,223 0.47− 2.50 < and≤ − 1 8,593 3.31− 1 < and< 0 69,659 26.85

Par Bonds Par = 0 63,400 24.43

Premium Bonds 0 < and≤ 1 19,072 7.351 < and≤ 2.50 34,542 13.312.50 < and≤ 5 24,928 9.615 < and≤ 10 24,143 9.30

10 < and≤ 15 10,712 4.1315 < and≤ 20 1,987 0.77≥ 20 701 0.27

All Bonds 259,471 100.00

The table lists a breakdown of issue prices (original issue discount, par, and premium bonds) relative to $100par value, which is denoted by zero. For example, the rst line of the table shows that 0.04% of bonds in oursample were deep discount bonds issued at a price $20 below par.

43



Table 3: Yield Spreads Across Different Price Bins

> 1 (0.5 1] [0 0.5] (RP DM ) (-0.5 0] (-1 -0.5] ≤ -1 # of Days

Panel A: Yield Spreads

All Trades -3.19 -0.15 1.73 3.73 26.52 37.70 61.78 2101(0.08) (0.23) (0.33) (0.30) (0.82) (1.05) (1.58)

# Trades per day 1528 114 129 153 45 32 108

Ask Trades -15.87 -17.94 -15.81 -15.18 -5.53 2.16 20.81 989(0.12) (0.23) (0.26) (0.39) (0.93) (1.11) (1.46)

# Trades per day 1025 87 110 96 25 20 70

Bid Trades 13.99 26.35 30.32 24.81 49.42 60.07 77.55 1372(0.14) (0.41) (0.48) (0.39) (0.96) (1.25) (1.62)

# Trades per day 492 40 44 56 24 18 56

Interdealer Trades 1.20 1.54 1.18 1.77 16.00 25.45 44.01 1758(0.10) (0.25) (0.27) (0.24) (0.62) (0.86) (1.13)

# Trades per day 464 39 43 74 19 13 46

Panel B: After-Tax Yield Spreads

All Trades -3.19 -0.15 1.73 1.10 12.48 16.68 27.58(0.09) (0.23) (0.34) (0.31) (0.82) (1.01) (1.39)

Ask Trades -15.87 -17.94 -15.81 -17.50 -18.80 -16.80 -8.87(0.13) (0.24) (0.26) (0.40) (0.93) (1.09) (1.32)

Bid Trades 14.00 26.36 30.32 22.19 35.16 38.00 40.82(0.14) (0.41) (0.49) (0.40) (0.94) (1.18) (1.45)

Interdealer Trades 1.21 1.55 1.19 -1.00 2.08 4.94 11.25(0.11) (0.26) (0.27) (0.26) (0.62) (0.82) (1.04)

The table reports average yield spreads and after-tax yield spreads for bonds partitioned into different pricebins. The seven bins are based on the distance between the bond price and the revised price (RP ) or deminimis boundaries (DM ). The three bins containing bond trades with prices higher thanRP are denedas: bin 1 (>1) with prices greater than $1.00 aboveRP ; bin 2 (0.5,1] with prices between $0.50 and $1.00(including $1) dollar aboveRP ; bin 3 [0 0.5] with prices between $0 and $0.50 (including $0 and $0.50)aboveRP ; bin 4 (RP DM ) which includes trades with prices betweenRP and DM ; bin 5 (-0.5 0] withprices from $0.00 to $0.5 (including $0.00) belowDM ; bin 6 (-1 -0.5] with prices from $0.50 to $1.00 belowDM ; and the last bin 7 (≤ − 1) contains all the prices more than $1.00 belowDM . In Panel A, the yieldspread is dened as the actual transaction yield minus the model-implied yield (the yield implied by valuingthe bond cashows using the municipal zero-coupon yield curve on that trading day). In Panel B, the after-tax yield spread is computed as the difference between the after-tax transaction yield and the model-impliedyield. All spreads are reported in basis points. In computing averages, we only include days for which at leastone trade takes place in all the bins. We also report the number of days for each type of trade used to computethe average and the average number of trades per day for each bin. We report standard errors in parentheses.

44



Table 4: Empirical Duration Across Different Price Bins

> 1 (0.5 1] [0 0.5] (RP DM ) (-0.5 0] (-1 -0.5] ≤ -1

All Trades

Empirical DurationD 7.00 4.58 3.47 6.31 6.62 6.52 7.31Model DurationD m 4.88 4.17 4.15 5.50 4.16 4.59 5.70D − D m 2.12 0.41 -0.68 0.81 2.46 1.93 1.62

( 0.09) ( 0.16) ( 0.04) ( 0.13) ( 0.51) ( 0.50) ( 0.19)

Interdealer Trades

Empirical DurationD 6.99 4.62 3.87 5.57 6.39 5.78 7.34Model DurationD m 5.13 4.30 4.24 5.43 4.20 4.60 5.64D − D m 1.86 0.31 -0.37 0.14 2.19 1.18 1.70

( 0.13) ( 0.11) ( 0.07) ( 0.12) ( 0.64) ( 0.27) ( 0.30)

In the table we report the empirical duration and model duration of bonds partitioned into different price bins.The seven bins are based on the distance between the bond price and the revised price (RP ) or de minimis

boundaries (DM ). The three bins containing bond trades with prices higher thanRP are dened as: bin 1(>1) with prices greater than $1.00 aboveRP ; bin 2 (0.5,1] with prices between $0.50 and $1.00 (including$1) dollar aboveRP ; bin 3 [0 0.5] with prices between $0 and $0.50 (including $0 and $0.50) aboveRP ;bin 4 (RP DM ) which includes trades with prices betweenRP and DM ; bin 5 (-0.5 0] with prices from$0.00 to $0.5 (including $0.00) belowDM ; bin 6 (-1 -0.5] with prices from $0.50 to $1.00 belowDM ; andthe last bin 7 (< − 1) contains all the prices more than or equal to $1.00 belowDM . The empirical durationof a trade is computed if the previous trade of the bond occurs within the past 30 days and the price level of the last trade occurs in the same tax region as the current trade following equation (8). Bins 1-3 represent theno-tax region, bin 4 is the capital gains tax region, and bins 5-7 are the income tax regions. Similarly, themodel-implied duration is computed using bond prices and yields implied from the zero coupon yield curveusing equation (9). We report standard errors of the difference between empirical duration and model impliedduration,D − D m , in parentheses.

45



Table 5: Controls for Default Risk

Panel A: Taking Only Short Maturity Bonds

> 1 (0.5 1] [0 0.5] (RP DM ) (-0.5 0] (-1 -0.5] ≤ -1 # of Days

Maturity 1-2 Years -8.54 -1.08 5.96 11.98 21.24 34.72 63.19 1247(0.32) (0.57) (0.75) (0.93) (1.24) (1.57) (2.08)

# Trades per Day 195 39 43 20 20 12 13

Panel B: Taking Only Insured Bonds

> 1 (0.5 1] [0 0.5] (RP DM ) (-0.5 0] (-1 -0.5] ≤ -1 # of Days

Insured -4.08 -1.79 -0.26 -0.97 7.29 11.55 17.02 1900(0.10) (0.24) (0.31) (0.32) (0.73) (0.97) (1.16)

# Trades per Day 968 76 87 106 31 23 78

Panel C: Taking Only Bonds from the Same Series

aboveRP (RP DM ) belowDM # of Days

All Trades -5.35 10.39 24.11 1658(0.75) (0.99) (1.13)

# Series per Day 14 12 10

The table reports average after-tax yield spreads (the difference between the after-tax transaction yield and themodel-implied yield) for bonds of different types partitioned into differentprice bins, representing default riskcontrols. Panel A takes only bonds of maturity between 1-2 years, while Panel B takes only insured bonds.Panel C considers only bonds of the same issue series, which are issued by the same issuer on the same date.In Panels A and B, the seven bins are based on the distance between the bond price and the revised price(RP ) or de minimis boundaries (DM ). The three bins containing bond trades with prices higher thanRP are dened as: bin 1 (>1) with prices greater than $1.00 aboveRP ; bin 2 (0.5,1] with prices between $0.50and $1.00 (including $1) dollar aboveRP ; bin 3 [0 0.5] with prices between $0 and $0.50 (including $0 and$0.50) aboveRP ; bin 4 (RP DM ) which includes trades with prices betweenRP andDM ; bin 5 (-0.5 0]with prices from $0.00 to $0.5 (including $0.00) belowDM ; bin 6 (-1 -0.5] with prices from $0.50 to $1.00

belowDM ; and the last bin 7 (< − 1) contains all the prices more than or equal to $1.00 belowDM . For thethree bins in Panel C, the rst bin contains bond trades with prices greater thanRP (bins 1-3); the second bin(RP DM ) includes trades with prices betweenRP andDM (bin 4); and the last bin contains prices belowDM (bins 5-7). In computing averages in each panel, we only include days for which at least one trade takesplace in all the bins. We also report the number of days for each type of trade used to compute the averageand the average number of series per day in each price bin. We report standard errors in parentheses.

46



Table 6: Controls for Liquidity

Panel A: Taking Only NY and CA Bonds

> 1 (0.5 1] [0 0.5] (RP DM ) (-0.5 0] (-1 -0.5] ≤ -1 # of Days

NY and CA -6.00 -3.03 -1.47 -0.82 3.54 6.36 12.08 1463(0.26) (0.41) (0.42) (0.39) (0.79) (0.98) (1.14)

# Trades per Day 451 33 38 45 14 10 34

Panel B: Excluding 1995, 1999-2000

> 1 (0.5 1] [0 0.5] (RP DM ) (-0.5 0] (-1 -0.5] ≤ -1 # of Days

Exclude 1995, 1999, 2000 -1.68 2.03 3.84 2.92 16.71 22.15 37.07 1409(0.05) (0.29) (0.45) (0.42) (1.12) (1.37) (1.90)# Trades per Day 1774 82 86 103 27 18 42

Panel C: Controlling for Transaction Size

> 1 ≤ -1 # of Days

All Trades 1.59 27.83 2095(0.20) (1.39)

# Trades per Day 105 105Average Par Amount Traded per Day $63,465 $63,465

The table reports average after-tax yield spreads (the difference between the after-tax transaction yield andthe model-implied yield) for bonds of different types partitioned into different price bins, representing defaultrisk controls. Panel A takes only New York and California bonds. Panel B excludes the years 1995, 1999,and 2000 from our sample. Panel C controls for trade size. In Panels A and B, the seven bins are based onthe distance between the bond price and the revised price (RP ) or de minimis boundaries (DM ). The threebins containing bond trades with prices higher thanRP are dened as: bin 1 (>1) with prices greater than$1.00 aboveRP ; bin 2 (0.5,1] with prices between $0.50 and $1.00 (including $1) dollar aboveRP ; bin 3 [00.5] with prices between $0 and $0.50 (including $0 and $0.50) aboveRP ; bin 4 (RP DM ) which includestrades with prices betweenRP and DM ; bin 5 (-0.5 0] with prices from $0.00 to $0.5 (including $0.00)belowDM ; bin 6 (-1 -0.5] with prices from $0.50 to $1.00 belowDM ; and the last bin 7 (< − 1) contains

all the prices more than or equal to $1.00 belowDM . The two bins in Panel C are bins 1 and 7 of PanelsA and B. In Panel C, we match a trade in bin 7 with a trade in bin 1 of exactly the same par amount traded.If no matching trade is found, we do not consider that transaction. If there is more than one trade in bin 1with the same par value traded as the trade in bin 7, we take a random trade of the same transaction size. Incomputing averages in each panel, we only include days for which at least one trade takes place in all thebins. We also report the number of days for each type of trade used to compute the average and the averagenumber of series per day in each price bin. We report standard errors in parentheses.

47



Table 7: Characterizing the Below De Minimis Yield Spread

Variable Coefcient T-statistic

Intercept 84.66 18.62

Log Par Amount -8.12 -176.23Maturity in Years -2.12 -107.41Distance toDM 1.22 44.62Issue Price 0.27 5.90

Selected Fixed Effects

Dummy General Obligation -6.17 -28.95Dummy Revenue 1.71 8.34Dummy Insured 1.45 10.01Dummy AAA -25.32 -109.64Dummy AA -22.61 -103.17Dummy Bid 15.99 123.80

Dummy Ask -23.42 -173.79

In this table we regress theyield spreadof bonds, denedas theactual transaction yield less themodel-impliedyield in basis points, involving all transactions involving below de minimis bonds onto various independentvariables. There are 405,871 transactions in total with prices below the de minimis bound. The average yieldspread for this sample is 27 basis points. “Distance to DM” refers to the value of DM − P measured indollars per $100 face value and “Issue Price” is also measured as per $100 face value. The regression alsoincludes separate dummies for each year (1995 to 2004) and separate dummies for the eight largest states interms of transactions (CA, NY, FL, TX, NJ, MI, OH, and PA). The “Dummy AA” is equal to 1 if a bond hasa rating of AA+, AA, or AA-.

48



Table 8: Events when Bonds Cross Between No-Tax and Capital Gains Tax Regions

Y last Y 0 ∆ Y 0 ∆ Y 0 ,τ ∆ Y m0 # of Trades

Panel A: All Trades

Crossing Down 4.19% 4.45% 26.76 24.74 0.46 13953(0.01%) (0.01%) (0.22) (0.21) (0.04)

Crossing Up 4.46% 4.09% -36.57 -34.15 -0.32 44198(0.00%) (0.00%) (0.13) (0.13) (0.02)

Crossing Down on the Same Day 4.24% 4.44% 20.84 18.99 0.00 32583(0.00%) (0.00%) (0.11) (0.10)

Crossing Up on the Same Day 4.40% 4.15% -24.47 -22.46 0.00 46627(0.00%) (0.00%) (0.10) (0.10)

Panel B: Ask Trades

Crossing Down 4.08% 4.24% 16.21 14.66 0.67 5867(0.01%) (0.01%) (0.18) (0.17) (0.06)

Crossing Up 4.28% 4.10% -17.52 -15.90 -0.43 6524(0.01%) (0.01%) (0.20) (0.20) (0.05)



Panel C: Bid Trades

Crossing Down 4.41% 4.77% 35.51 33.24 0.44 1743(0.02%) (0.02%) (0.67) (0.66) (0.11)

Crossing Up 4.70% 4.33% -37.02 -34.70 -0.44 2076(0.02%) (0.02%) (0.65) (0.64) (0.10)



Panel D: Interdealer Trades

Crossing Down 4.45% 4.61% 15.85 14.21 0.97 2625(0.01%) (0.01%) (0.31) (0.30) (0.11)

Crossing Up 4.58% 4.37% -20.19 -18.36 -1.07 5675(0.01%) (0.01%) (0.26) (0.25) (0.06)Crossing Down on the Same Day 4.46% 4.64% 18.34 16.61 0.00 7547

(0.01%) (0.01%) (0.20) (0.19)Crossing Up on the Same Day 4.64% 4.48% -16.75 -15.10 0.00 6802

(0.01%) (0.01%) (0.20) (0.19)

49



Note to Table 8The table lists averages of yields and yield changes for events where bonds cross between the no-tax regionand the capital gains tax region, with boundaries of revised issue price,RP , and the de minimis boundary,DM . We denote the event time of the transaction crossing theRP boundary as time zero and report the yieldin the column labeled “Y 0 .” The yield of the prior trade is denoted asY last . We only consider bonds enteringor leaving the capital gains tax region to the no-tax region, with no below de minimis trades counted. Wereport the change in yield∆ Y 0 = Y 0 − Y last . The change in the after-tax yields between the event trade andthe prior trade is reported as∆ Y 0 ,τ = Y 0 ,τ − Y last,τ . We also report the change in the model-implied tax-exempt yields,∆ Y m0 = Y m0 − Y mlast , which is zero for intra-day trades. All the columns with yield changesare expressed in basis points. We subdivide by the transaction type in Panels A-D. For Panel B (C), the eventtrade and the trade prior to the event both occur at the bid (ask), and in Panel D, the event trade and thetrade prior are both interdealer trades. For the rows labeled “Crossing Down” and “Crossing Up,” we trackall events where bonds move down or up, respectively, across the revised price boundary with the last tradehappening within the previous ve days (but not the same day as the cross). For the rows labeled “CrossingDown on the Same Day” and “Crossing Up on the Same Day,” the last trade occurs on the same trading dayas the cross. We report the number of trades in each category in the last column and report standard errors inparentheses.

50



Table 9: Events when Prices Cross Into or Out of the Income Tax Region

Y last Y 0 ∆ Y 0 ∆ Y 0 ,τ ∆ Y m0 # of Trades

Panel A: All Trades

Crossing Down 4.22% 4.79% 57.19 38.86 0.55 8979(0.01%) (0.01%) (0.51) (0.42) (0.05)

Crossing Up 4.78% 4.14% -63.57 -43.72 -0.24 42528(0.00%) (0.00%) (0.22) (0.18) (0.02)



Panel B: Ask Trades

Crossing Down 4.02% 4.33% 31.24 17.99 0.81 2339(0.02%) (0.02%) (0.66) (0.53) (0.09)

Crossing Up 4.38% 4.01% -36.50 -22.11 -0.44 2784(0.02%) (0.02%) (0.73) (0.59) (0.08)



Panel C: Bid Trades

Crossing Down 4.50% 5.14% 63.46 42.98 0.55 2099(0.01%) (0.02%) (1.03) (0.83) (0.11)

Crossing Up 5.05% 4.42% -63.45 -43.10 -0.49 2354(0.02%) (0.01%) (0.98) (0.80) (0.10)



Panel D: Interdealer Trades

Crossing Down 4.45% 4.74% 29.46 17.00 0.98 1477(0.02%) (0.02%) (1.07) (0.82) (0.14)

Crossing Up 4.75% 4.38% -37.03 -22.81 -0.94 4329(0.01%) (0.01%) (0.54) (0.44) (0.08)Crossing Down on the Same Day 4.53% 4.84% 30.96 17.82 0.00 5914

(0.01%) (0.01%) (0.39) (0.29)Crossing Up on the Same Day 4.87% 4.57% -30.54 -17.65 0.00 5161

(0.01%) (0.01%) (0.51) (0.40)

51



Note to Table 9The table lists averages of yields and yield changes for events where bonds cross the de minimis boundary,DM . We denote the event time of the rst transaction crossing theDM boundary as time zero and reportthe yield in the column labeled “Y 0 .” The yield of the prior trade is denoted asY last . We report the changein yield∆ Y 0 = Y 0 − Y last . The change in the after-tax yields between the event trade and the prior tradeis reported as∆ Y 0 ,τ = Y 0 ,τ − Y last,τ . We also report the change in the model-implied tax-exempt yields,∆ Y m0 = Y m0 − Y mlast , which is zero for intra-day trades. We take only trades where the de minimis boundarydoes not change across the last trade to the event trade, thus the cross is due to the change in bond prices,not due to a shifting de minimis boundary. All the columns with yield changes are expressed in basis points.We subdivide by the transaction type in Panels A-D. For Panel B (C), the event trade and the trade prior tothe event both occur at the bid (ask), and in Panel D, the event trade and the trade prior are both interdealertrades. For the rows labeled “Crossing Down” and “Crossing Up,” we track all events where bonds movedown or up, respectively, across the de minimis boundary with the last trade happening within the previousve days (but not the same day as the cross). For the rows labeled “Crossing Down on the Same Day” and“Crossing Up on the Same Day,” the last trade occurs on the same trading day as the cross. We report thenumber of trades in each category in the last column and report standard errors in parentheses.

52



Table 10: Estimating Implied Tax Rates

Panel A: Implied Income Tax Rates

IncomeTrade Type Tax Rate Std Error # of Obs

All 0.79 0.01 29581Ask 0.73 0.03 4320Bid 1.20 0.02 2647Interdealer 1.01 0.02 7391

Panel B: Implied Capital Gains Tax Rates

Capital GainsTrade Type Tax Rate Std Error # of Obs

All -0.04 0.01 39391Ask 0.01 0.04 3884Bid 0.20 0.07 1529

Interdealer -0.09 0.03 7573

In Panel A, we use the rst trades of bonds in the below de minimis region when the bond rst becomessubject to income tax to estimate the implied tax rateτ I using equation (10). In Panel B, we use the rsttrades of bonds in the capital gains region (fromRP to DM ) to estimate the implied capital gains tax rateτ C in equation (11). We only use observations where the prior trade before the crossover happens within 5days, including when the last trade occurs on the same day as the trade crossing the de minimis or revisedprice boundaries. In Panels A and B, for the ask, bid, and interdealer trade types, we take only those tradeswhere the previous trade with the previous 5 days is of the same trade type. In estimatingτ I andτ C , we usexed effects for each year; dummies for different bond types (general obligation or revenue); dummies fordifferent original issue prices (par or premium); and dummies for the eight most traded states (CA, NY, FL,TX, NJ, MI, OH, and PA).

53



Figure 1: Illustration of Market Discount for an OID Bond

0 1 2 3 4 5 6 7 8 9 1084

86

88

90

92

94

96

98

100

Years to Maturity

B o n d P r i c e

Accreted OID at 12%De Minimis boundaryPurchase Price = 84Accreted Purchase Price at 13.3105%Redemption Price = 100

Consider an OID bond originally issued with a 10-year maturity paying a 10% semi-annual coupon. Att = 0 ,this bond is issued at a price of $88.5301 with a par value of 100. The semi-annual initial yield at issue of this bond is 12%. The solid line plots the accreted OID of this bond, also called the revised price of the bond,which is the value of the remaining payments of the bond discounted at its original 12% yield. At timet = 2 ,an investor purchases this bond in the secondary market at a price of $84. Att = 2 , the revised issue priceof the bond is $89.8941, which is equivalent to the original issue price of $88.5301 plus $1.3640 in accretedOID. The market discount att = 2 is the difference between the revised issue price and the purchase price,which is89.8941 − 84.0000 = $5 .8941 and graphed as a solid vertical line att = 2 . The plot also shows theaccreted purchase price of $84 fromt = 2 to the redemption value of $100 att = 10 , representing accretionat a yield of 13.3105%, in the dashed line and the de minimis boundary in black dots.

54



Figure 2: Holdings of Municipal Bonds

1950 1960 1970 1980 1990 2000 20100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Households Direct and IndirectBanksInsurance Cos

This gure plots the percentage of outstanding municipal bonds held by households, which includes directownership and indirect ownership through mutual funds, money market funds, and closed-end funds; banks,

which comprise commercial banks and savings institutions; and insurance companies, which are life insur-ance companies and other insurance companies. The computations are the authors’ own using raw data fromthe Flow of Funds compiled by the Federal Reserve.

55



Figure 3: Trades of Municipal Bonds

Number of Bonds Each Month

1994 1996 1998 2000 2002 2004 20060

10

20

30

40

50

60

70

80

90

N u m

b e r o

f B o n

d s

i n T h o u s a n

d s

Proportion of Bonds Trading Below De Minimis

1994 1996 1998 2000 2002 2004 20060

0.1

0.2

0.3

0.4

0.5

P e r c e n t a g e o f T r a d e s B e l o w d e M i n i m i s

1994 1996 1998 2000 2002 2004 20060.01

0.02

0.03

0.04

0.05

0.06

5 −

Y r Z e r o R a t e

In the top panel, we plot the total number of trades each month in our sample, totalling 5,372,631 over January1995 to November 2005. The bottom panel plots the proportion of trades below the de minimis boundaryeach month, as a fraction of the total amount of trades in that month, in the solid line. In the dashed line, weplot the 5-year zero-coupon municipal bond yield, which is computed using the method detailed in Section3.3.

56





Figure 5: Additional Yields Required by Below De Minimis Bonds

0 0.01 0.02 0.03 0.04 0.05 0.060

20

40

60

80

100

120

140

160

180

Maturity = 10 years

Maturity = 5 years

Maturity = 2 years

We consider par bonds of different maturities paying semi-annual coupons of 2.35%. For a given tax-exemptyield (on thex -axis), we compute the additional yield (in basis points on they-axis) above the tax-exemptyield required to obtain the same IRR on the after-tax cashows as the tax-exempt yield. We assume thatτ I = 0 .35 andτ C = 0 .15.

58



Figure 6: Yields across Different Price Bins

>1 (0.5 1] [0 0.5] (RP DM) (−0.5 0] (−1 −0.5] <−13.6

3.8

4

4.2

4.4

4.6

4.8All prices

YieldModel Yield

>1 (0.5 1] [0 0.5] (RP DM) (−0.5 0] (−1 −0.5] <−13.6

3.8

4

4.2

4.44.6

4.8Ask prices

Yield

Model Yield

>1 (0.5 1] [0 0.5] (RP DM) (−0.5 0] (−1 −0.5] <−13.6

3.8

4

4.2

4.4

4.6

4.8Bid prices

YieldModel Yield

>1 (0.5 1] [0 0.5] (RP DM) (−0.5 0] (−1 −0.5] <−13.6

3.8

4

4.2

4.4

4.6

Interdealer prices

YieldModel Yield

59



Note to Figure 6We plot average yields and average model-implied yields across different price buckets with two standarderror bands given by the dotted lines. We divide all the transactions into seven bins based on the distancebetween the bond price and the revised price (RP ) or de minimis boundaries (DM ). The three bins contain-ing bond trades with prices higher thanRP are dened as: bin 1 (>1) with prices greater than $1.00 aboveRP ; bin 2 (0.5,1] with prices between $0.50 and $1.00 (including $1) dollar aboveRP ; bin 3 [0 0.5] withprices between $0 and $0.50 (including $0 and $0.50) aboveRP ; bin 4 (RP DM ) which includes tradeswith prices betweenRP andDM ; bin 5 (-0.5 0] contains prices from $0.00 to $0.5 (including $0.00) belowDM ; bin 6 (-1 -0.5] has prices from $0.50 to $1.00 belowDM ; and the last bin 7 (< − 1) contains all theprices more than $1.00 belowDM . We plot averages across days where at least one trade takes place in allthe bins.

60



Figure A-1: Illustration of Market Discount for Bonds Sold Prior to Maturity

Case of a Par Bond

0 1 2 3 4 5 6 7 8 9 1094

95

96

97

98

99

100

101

Years to Maturity

B o n d P r i c e

Accreted OID at 10%De Minimis boundaryPurchase Price = 95Accreted Purchase Price at 10.9543%Sale Price = 99

Case of an OID Bond

0 1 2 3 4 5 6 7 8 9 1084

86

88

90

92

94

96

98

100

Years to Maturity

B o n d P r i c e

Accreted OID at 12%De Minimis boundaryPurchase Price = 84Accreted Purchase Price at 13.3105%Sale Price = 99

61



Note to Figure A-1The gure illustrates the taxation of market discount for a bond sold prior to maturity. We consider thecase of a par bond in the top panel and an OID bond in the bottom panel. In the top panel, consider a parbond originally issued with a 10-year maturity paying a 10% semi-annual coupon (Bond A). The top panelillustrates the case of a market transaction comprising both income and capital gain components. Att = 2 ,Bond A is sold at a price of $95 representing a yield of 10.9543%. This point is denoted as a diamond in thegure. The dashed line plots the accreted discount of the $95 purchase price (the revised price) to maturity ata yield of 10.9543%. This accretion is taxed as income. Att = 8 , the bond is sold for a price of $99, which isdenoted by a square. The revised price of Bond A att = 8 is $98.3266. The gain in excess of the accretion of market discount is the distance between the red square and the dashed line, which is $0.6734, which is taxedas a capital gain. The remaining $3.3266, which is the accretion of market discount, is taxed as income. Inthe bottom panel, consider Bond B, which is an OID bond originally issued with a 10-year maturity payinga 10% coupon. Bond B was issued at a price of $88.5301 with a par value of 100 with an initial yield of 12%. The accretion of OID fromt = 0 is shown in the solid blue line. Suppose that at timet = 2 , BondB is purchased for $84 at a yield of 13.3105%, which is denoted by the red diamond. The accretion of thispurchase price at 13.3105% is shown in the dashed red line. Att = 8 , Bond B is sold for $99, denoted in thegure as a red square. The rst vertical line att = 2 represents the market discount at purchase. The secondvertical line att = 8 represents the market discount at sale. The difference between the two vertical linesrepresents the accrued market discount at the time of sale, which is taxed as income at the time of sale.

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Taxes on Tax-Exempt Bonds