Printer Friendly

Implicit taxes: evidence from taxable, AMT, and tax-exempt state and local government bond yields.

ABSTRACT

Pretax yields of state and local government (SALG) bonds are examined for evidence of implicit taxes. The sample includes fully taxable bonds, alternative minimum tax (AMT) bonds (tax-exempt but a tax preference for alternative minimum tax purposes), and tax-exempt bonds (tax-exempt and not a tax preference for AMT purposes). The average risk-adjusted pretax yield on AMT bonds is higher than that of tax-exempt bonds and lower than that of taxable bonds. Implicit taxes are estimated at 25.23 to 29.68 percent for AMT bonds and 33.87 to 35.27 percent for tax-exempt bonds. Results indicate that asset prices are affected by the AMT system and that marginal investors in AMT bonds assess a positive probability (between 28 and 45 percent) of being subject to the AMT. Estimated implicit tax rates on longer-term tax-exempt bonds are higher when yields are compared to those of taxable SALG bonds rather than taxable U.S. Treasury securities.

Data Availability: Contact the author.

INTRODUCTION

This paper examines pretax yields on state and local government (SALG) bonds for evidence of implicit taxes associated with the regular income tax and the alternative minimum tax (AMT) systems. SALG bonds may be taxed in one of three ways: fully taxable, tax-exempt but a tax preference for AMT purposes (hereafter referred to as "AMT bonds"), or tax-exempt and not a tax preference for AMT purposes (hereafter referred to as "tax-exempt bonds"). I examine whether implicit taxes differ for tax-exempt bonds and AMT bonds by comparing risk-adjusted pretax yields across the three types of SALG bonds. In addition, I examine whether implicit tax rates on longer-term tax-exempt SALG bonds are higher when compared to taxable SALG bonds of the same maturities rather than U.S. Treasury security index yields.

Prior research indicates that estimated implicit tax rates on shorter-term tax-exempt securities are close to the corporate statutory tax rate, while implicit tax rates on longer-term securities are much lower. This finding is referred to as the "muni puzzle." (1) These studies generally use U.S. Treasury security index yields as the taxable security benchmark for estimating implicit tax rates. I am not aware of any prior studies that have used taxable SALG bond yields as the taxable security benchmark for estimating implicit tax rates in tax-exempt SALG bond prices.

Prior research examining implicit taxes in asset prices focuses on the regular income tax system. The AMT system has a broader base and lower tax rates than the regular tax system. Investors must pay the AMT only if the tax computed under this alternative system is greater than that computed under the regular tax system. At the time an AMT bond is purchased, investors cannot know with certainty whether they will be required to pay tax on the interest income received. Thus, the implicit tax impounded in AMT bond prices will be a function of the investor's assessed probability of being subject to the AMT. The probability of a taxpayer being subject to the AMT was low when the AMT was first enacted. This probability has increased substantially in recent years primarily because the AMT tax brackets have remained constant while the regular tax brackets have been indexed for inflation each year and recently reduced without corresponding reductions in the AMT tax brackets. (2) However, investors who assess a relati vely high probability of being subject to the AMT may choose not to invest in AMT bonds. Thus, there is a great deal of uncertainty regarding the impact of the AMT on asset prices. I am not aware of any prior studies that have examined whether the AMT system affects asset prices.

In this paper, I identify a sample of taxable SALG bonds to use as a benchmark for measuring implicit taxes in tax-exempt and AMT bonds. I control for differences in bond ratings, call options, sinking fund requirements, insurance, and years-to-maturity across bond issues. I find that the average risk-adjusted yield on tax-exempt bonds is lower than that of AMT bonds and taxable bonds. In addition, the average risk-adjusted yield on AMT bonds is lower than that of taxable bonds. I estimate that implicit taxes are 33.87 to 35.27 percent on tax-exempt bonds and 25.23 to 29.68 percent on AMT bonds. My results suggest that marginal investors in AMT bonds are individuals who assess a positive probability of being subject to the AMT (approximately 40 to 45 percent for the July 20, 2001 sample and 28 to 31 percent for the May 1, 2002 sample). The results are similar when bond issues that mature in less than two years are deleted from the sample. Thus, the estimated 33.87 to 35.27 percent implicit tax rate holds for longer-term tax-exempt SALG bonds.

To further investigate whether estimated implicit tax rates are higher when taxable SALG bonds are used as benchmark securities rather than U.S. Treasury securities, I first regress tax-exempt SALG bond yields on an index of U.S. Treasury security yields (matched by maturity) and estimate an implicit tax rate of only 14.2 percent. I then regress the same tax-exempt SALG bond yields on taxable SALG bond yields (matched by maturity) and estimate an implicit tax rate of 34.9 percent, which is consistent with the results discussed above.

This study makes three contributions to the implicit tax literature. First, I provide evidence that the AMT system affects asset prices. My results suggest that research examining implicit taxes must consider potential AMT effects for those items that are taxed differently under the regular tax and AMT systems. For example, the 70 percent dividends-received deduction (DRD) is included in the computation of adjusted current earnings for corporations in the same manner as tax-exempt interest income [I.R.C. (ss)56(g)(4)(C)]. As a result, implicit taxes associated with the DRD may be lower than would otherwise be predicted by theory that is based on the regular income tax rules alone.

Second, I provide evidence that marginal investors in AMT bonds are individuals who assess a positive probability (between 28 and 45 percent) of being subject to the AMT. Under the Scholes and Wolfson (1992) framework, investors who do not expect to pay the AMT would be expected to form a clientele to invest in AMT bonds. The results of this study suggest this did not occur. Scholes et al. (2002) discuss how the joint presence of transaction costs and uncertainty with respect to future tax status can influence the formation of tax clienteles. My results suggest that uncertainty regarding the applicability of the AMT impedes the development of tax clienteles for AMT bonds.

Third, I provide evidence that estimated implicit taxes on tax-exempt SALG bonds are much higher when taxable SALG bonds are used as benchmark securities rather than U.S. Treasury security indexes. This occurs without controlling for differences in bond features such as ratings, call options, insurance, sinking fund requirements, or years-to-maturity. My analysis of the relation between taxable SALG bonds yields and maturity-matched U.S. Treasury security index yields suggests that mandatory sinking fund requirements indicate higher default risk that is not captured by bond ratings. Furthermore, the positive mean difference between taxable SALG bond yields and maturity-matched U.S. Treasury security index yields (after controlling for ratings, call provisions, and sinking fund requirements) suggests that higher SALG bond yields are only partially explained by these specific bond features. The decentralized market for SALG bonds and higher information search costs may contribute to the "muni puzzle."

The remainder of the paper is organized as follows. The first section discusses prior research. The second section discusses the federal and state income taxation of SALG bonds. The third section develops predictions for the relations between the pretax yields of taxable, AMT, and tax-exempt SAIG bonds. The fourth section describes the sample selection procedure and presents the methods employed in testing the hypotheses. Results are presented in the fifth section and the last section summarizes the results and provides concluding remarks.

PRIOR RESEARCH

A major area of current tax research in accounting involves investigations into the effects of taxes on asset prices. Studies in the accounting literature have examined T-bill yield spreads (Guenther 1994), leveraged ESOPs (Shackelford 1991), preferred stock prices (Erickson and Maydew 1998; Atwood 2002), and common stock prices (summarized in Shackelford and Shevlin 2001) for evidence of implicit taxes.

Chalmers (1998) suggests that SALG bond yields are a worthwhile area for examining the role of taxes in asset prices for two reasons. First, they comprise a significant segment of the U.S. capital market ($1.3 trillion in 1995). Second, prior research has not yet been able to explain the role of taxes in the pricing of tax-exempt bonds. Unlike equity securities, SALG bond cash payout amounts are fixed and the payment dates are known, minimizing the problems associated with determining expected pretax cash flows. A better understanding of implicit taxes in SALG bond yields might provide insights that are helpful in determining the role of taxes in the pricing of other assets.

SALG bonds are also a worthwhile area for examining the role of taxes in asset prices for a third reason. SALG bonds are taxed in three different ways (fully taxable, AMT, or tax-exempt) but are more homogenous along nontax dimensions than other assets that are taxed differentially. This fact allows for a cleaner test of implicit taxes in SALG bond yields than is possible when examining other types of financial assets.

An implicit tax is defined as the reduced pretax return on a tax-favored asset that is necessary to make the marginal investor indifferent between investing in the tax-favored asset and a comparable taxable asset. (3) The classic example of implicit taxes in asset prices is the lower average pretax yield on tax-exempt bonds compared to taxable bonds. Miller (1977) predicts that, in a world with progressive individual income taxes and a fixed corporate tax rate, the implicit tax rate on tax-exempt bonds will equal the corporate tax rate. The magnitude of the implicit tax on tax-exempt bonds is difficult to measure empirically, however, because it requires identification of a comparable taxable bond to use as a benchmark.

Prior research has focused on measuring implicit taxes by comparing indexes of newly issued tax-exempt bond yields with those of U.S. Treasury securities or corporate bonds. These studies document implicit tax rates in very short-term tax-exempt bond yields that are close to the maximum statutory corporate tax rate (Jordan and Pettway 1985; Poterba 1986; Scholes and Wolfson 1992; Chalmers 1998). However, implicit tax rates in longer-term tax-exempt bond yields are much lower (Arak and Guentner 1983; Poterba 1986; Scholes and Wolfson 1992; Chalmers 1998). This finding is often referred to as the "muni puzzle."

Prior researchers have hypothesized that the low estimated marginal tax rate on longer-term tax-exempt bonds can be attributed to differences in risk and call options between tax-exempt bonds and the taxable securities that are used as benchmarks. However, the evidence provided by these studies is mixed and inconclusive (Buser and Hess 1986; Chalmers 1998; Skelton 1983; Stock 1994; Trzcinka 1982; Yawitz et al. 1985).

Chalmers (1998) examines tax-exempt SALG bonds that are backed by U.S. Treasury securities (which are effectively default free and noncallable). These tax-exempt SALG bond yields are regressed on U.S. Treasury security yields (matched by maturity) and the term-to-maturity. The coefficient on the term-to-maturity is positive and significant, indicating that the yields on longer-term SALG bonds are higher (i.e., the estimated implicit tax is lower) than theory would predict. He concludes that the lower implicit taxes on tax-exempt SALG bonds cannot be due to default risk or differences in call options as suggested by prior researchers.

The Tax Reform Act of 1986 (TRA 1986) imposed substantial restrictions and registration requirements that SALG bonds must meet in order to qualify as tax-exempt bonds. As a result, fully taxable SALG bonds now exist. The Bond Market Association's web site, http://www.bondmarkets.com, indicates that over $75 billion in taxable SALG bonds have been issued over the past five years. I am not aware of any prior studies that have used taxable SALG bonds as benchmark securities for measuring the implicit tax on tax-exempt SALG bonds.

The TRA 1986 also created the AMT system under which a portion of otherwise tax-exempt SALG bond interest income may be subject to tax. The AMT system has a broader base and lower tax rates than the regular income tax system. However, the AMT is imposed only when the tax calculated under that system is greater than the tax calculated under the regular income tax system. For this reason, investors do not know with certainty whether the interest received from AMT bonds will be subject to tax. Thus, there is a great deal of uncertainty regarding the impact of the AMT system on asset prices. I am not aware of any prior studies that have examined explicitly whether implicit taxes are affected by the AMT system.

TAXATION OF SALG BONDS

This section summarizes SALG bond taxation to provide insights on the differences between SALG bonds that have been determined to be taxable bonds, AMT bonds, or tax-exempt bonds. These rules are for non-dealer-investors (special rules apply to securities dealers).

Interest Income

Interest income from SALG bonds is generally exempt from federal income taxation [I.R.C. [section]103(a)]. However, three types of SALG bonds are fully taxable: (1) arbitrage bonds, defined as any bond issue where any portion of the proceeds is reasonably expected to be used to acquire higher yielding investments either directly or indirectly [I.R.C. [section]103(b)(2); I.R.C. [section]148]; (2) bonds that are federally guaranteed or that do not meet certain registration and information reporting requirements [I.R.C. [section]103(b)(3); I.R.C. [section]149]; and (3) nonqualified private activity bonds [I.R.C. [section]103(b)(1); I.R.C. [section]141].

Private activity bonds are SALG bonds where more than 10 percent of the proceeds are used directly or indirectly by an organization other than a governmental unit [I.R.C. [section]141]. Private activity bond proceeds must meet certain allowed uses to be tax-exempt for regular tax purposes.

Qualified uses include (1) providing airports, electric energy, gas, or water supply, or other specified uses [I.R.C. [ss]142]; (2) providing qualified owner-occupied residences [I.R.C. [ss]143]; (3) providing housing for veterans [I.R.C. [ss]143]; (4) providing for qualified capital improvements with small issues [I.R.C. [ss]144]; (5) providing qualified student loans [J.R.C. [ss]144]; (6) providing funds to improve designated "blighted areas" [I.R.C. [ss]144]; or (7) providing property for use by qualified tax-exempt organizations [I.R.C. [ss] 145].

In addition to the qualified use requirements, private activity bonds must meet volume cap requirements. The face amount of the private activity bond issue plus the aggregate of all private activity bonds previously issued during that calendar year cannot exceed the volume cap. For calendar 2001, the volume cap for a state issuer is $62.50 multiplied by that state's population [I.R.C. [ss]146]. Similar volume caps are imposed on state agencies and local jurisdictions.

Finally, private activity bonds must meet other requirements such as a limitation on length of maturity, a limitation on use for land acquisition, a prohibition from acquiring existing property, a prohibition against using the proceeds for skyboxes, airplanes, and gambling establishments, a restriction on financing issuance costs, and a requirement that public approval be obtained [I.R.C. [ss]147].

If a private activity bond fails to meet the qualified use, volume cap, or other requirements, then it is fully taxable for regular tax purposes. If a private activity bond meets all of these requirements, then it is tax-exempt for regular tax purposes. However, otherwise tax-exempt interest income from specified private activity bonds is a tax preference item in computing alternative minimum taxable income (AMTI) [I.R.C. [ss]57(a)(5)]. Specified bonds include all private activity bonds issued after August 7, 1986 that are not refunding bonds or qualified I.R.C. [ss]501(c)(3) bonds. (4)

For individual investors, interest income from SALG tax-exempt bonds is fully exempt from tax for both regular tax purposes and AMT purposes. However, for corporate investors, interest income from tax-exempt bonds is included in the calculation of Adjusted Current Earnings (ACE) [I.R.C. [ss]56(g)(4)(B)]. AMTI includes 75 percent of the excess of ACE over AMTI calculated before the ACE adjustment. Thus, 75 percent of interest income from SALG tax-exempt bonds is included in AMTI, while 100 percent of interest income from SALG AMT bonds is included in AMTI for corporate investors.

In summary, SALG bond interest is taxed under a complex body of rules and restrictions. In addition, there are numerous Revenue Procedures issued by the Internal Revenue Service to provide guidelines for requesting advanced rulings regarding the tax status of these bond issues. The majority of SALG bonds are tax-exempt or AMT bonds, however, the number of fully taxable bonds outstanding is sufficient to obtain a reasonable sample to use as a benchmark for examining implicit taxes in tax-exempt and AMT bonds.

Discounts and Premiums

The taxation of purchase discounts on taxable bonds depends on whether the discount was an original issue discount (OID) or a market discount. Investors in taxable bonds must include accrued original issue discount in income each year [I.R.C. [ss]1272(a)(1)]. Investors in taxable bonds purchased at a market discount are not taxed on the accrued market discount until maturity or sale unless the taxpayer elects to include the discount in income over the life of the bond [I.R.C. [ss]1278(b)(1)]. When accrued discount is included in income, the investor's basis increases by the amount of income recognized [I.R.C. [ss]1272(d)(2); I.R.C. [ss]1278(b)(4)].

For taxable bonds purchased at a premium, investors can elect to deduct premium amortization each year over the life of the bond [I.R.C. [section]171(a)(1)] and reduce the basis in the bond accordingly [I.R.C. [section]1016(a)(5)]. If no election is made, then the bond premium is included in the investor's basis and reduces the taxable gain (or increases the loss) upon the sale or maturity of the bond.

Investors in tax-exempt bonds make no adjustments to income over the life of the bond for accrued original issue discounts [I.R.C. [section]1272(a)(2)(A)] or accrued market discounts [I.R.C. [section]1278(b)(1)(C)]. However, the investor's basis in the bond increases each year by the amount of the accrued original issue discount [I.R.C. [section] 1288(a)]. In addition, investors in tax-exempt bonds cannot deduct bond premium amortization [I.R.C. [section]171(a)(2)]. However, the investor's basis in a tax-exempt bond is reduced each year for the amount of the disallowed premium amortization [I.R.C. [section]1016(a)(6)].

Gains and Losses

Gains and losses from the sale of taxable bonds before maturity are generally taxed as capital gains and losses. However, gain from the sale or maturity of a taxable market discount bond is ordinary to the extent of the market discount accrued since purchase (unless the investor elects to include the accrued discount in income each year) [I.R.C. [section]1276(a)]. Thus, investors can defer paying tax on a market discount but they cannot convert ordinary income to capital gain income by not recognizing the market discount currently.

Gain from the sale or maturity of a tax-exempt market discount bond is also ordinary to the extent of the market discount accrued since purchase [I.R.C. ??1276(a)]. Any additional gain is a capital gain and any loss is a capital loss. Thus, investors must pay tax on the market discount accrued since purchase on a tax-exempt bond, but the tax is deferred until the bond matures or is sold.

State Income Taxation of SALG Bonds

The Commerce Clearing House State Tax Guide (para. 15-150) provides a summary of state income taxation of interest income from SALG bonds. For resident individual taxpayers, most states exclude from their state income tax bases any interest income received from SALG bonds issued by their own state authorities and political subdivisions. Most states include in their state income tax bases any interest income from SALG bonds issued by other state authorities and their political subdivisions. Four states (Illinois, Iowa, Oklahoma, and Wisconsin) only exclude interest income from bonds issued by certain authorities within their states.

For corporate taxpayers, 11 states (Connecticut, Florida, Massachusetts, Minnesota, Montana, New Jersey, New York, Oregon, Tennessee, Utah, and West Virginia) include interest income from all SALG bonds in their state income tax bases. Four states (Illinois, Iowa, Oklahoma, and Wisconsin) only exclude interest income from bonds issued by certain authorities within their states. The remaining states exclude from their state income tax bases any interest income from bonds issued by their own state authorities and political subdivisions and include in their state income tax bases any interest income from bonds issued by other state authorities and political subdivisions.

HYPOTHESES DEVELOPMENT

Under federal income tax law, SALG bonds are tax-exempt, AMT, or fully taxable bonds. Predictions regarding expected differences in implicit taxes in tax-exempt and AMT bond yields depend on whether the marginal investor is a tax-exempt entity (such as a pension fund), an individual, or a corporation. In this study, it is not possible to distinguish ex ante whether the marginal investors in SALG bond are tax-exempt entities, corporations, or individuals. For this reason, I model the after-tax returns and discuss the expected ordering of pretax returns for each of these three potential investors.

A tax-exempt investor is indifferent between the three types of bonds only if the expected pretax returns are equal. Thus, the following relations will hold in equilibrium if the marginal investor is a tax-exempt entity: E([R.sub.e]) = E([R.sub.amt]) = E([R.sub.tax]) (1)

where R is the pretax return and the subscripts e, amt, and tax indicate the bond is a tax-exempt bond, an AMT bond, or a taxable bond, respectively.

For an individual investor to be indifferent between taxable bonds, AMT bonds, and tax exempt bonds, the expected after-tax returns must be equal. Interest income from tax-exempt bonds is not subject to tax regardless of whether the individual is subject to the AMT. Thus, the individual investor's expected after-tax return from a tax-exempt bond equals the expected pretax return as follows.

Individual investor in tax-exempt SALG bond:

E([r.sub.e,i]) = E([R.sub.e]) (2)

where r is the after-tax return, the subscript i indicates the marginal investor is an individual, and all other variables and subscripts are as previously defined.

An individual's after-tax return on a taxable bond or an AMT bond depends on whether that individual is subject to the AMT. Taxpayers are subject to the AMT for any year in which the tax calculated under the AMT system exceeds the tax calculated under the regular tax system. Investors can implement tax-planning strategies on a year-by-year basis in an attempt to avoid being subject to the AMT; however, they cannot know with certainty whether they will be subject to the AMT in future years. For this reason, I include the probability of being subject to the AMT in the models for the individual investor's expected return from taxable bonds and AMT bonds.

Interest income from an AMT bond is taxed only if the individual investor is subject to the AMT. The expected after-tax return from an AMT bond is as follows.

Individual investor in AMT bond:

E([r.sub.amt,i]) = E([R.sub.amt])(1 - [p.sub.i]) + E([R.sub.amt])(1 - [[tau].sub.a,i])[p.sub.i] = E([R.sub.amt])(1 - [[tau].sub.a,i] [p.sub.i]) (3)

where [[tau].sub.a] is the marginal tax rate for AMT purposes, p is the probability that the investor will be subject to the AMT, and all other variables and subscripts are as previously defined. (5)

Interest income from taxable bonds is included in regular taxable income and in alternative minimum taxable income (AMTI). The tax rate paid on the interest income depends on whether the individual is subject to the AMT. The individual investor's expected after-tax return from a taxable bond is as follows.

Individual investor in taxable SALG bond:

E([r.sub.tax,i]) = E([R.sub.tax])(1 - [[tau].sub.r,i])(1- [p.sub.i]) + E([R.sub.tax])(1 - [[tau].sub.a,i])[p.sub.i] = E([R.sub.tax])[1 - [[tau].sub.r,i](1 - [p.sub.i]) - [[tau].sub.a,i] x [p.sub.i]] (4)

where [[tau].sub.r] is the marginal tax rate for regular tax purposes and all other variables and subscripts are as previously defined.

In equilibrium, the after-tax return on SALG tax-exempt bonds, AMT bonds, and taxable bonds will be equal for the marginal investor. Equating the after-tax returns and solving for the ratio of the expected pretax returns, the relations between the expected pretax returns are as follows.

Taxable bonds vs. AMT bonds:

E([R.sub.amt])/E([R.sub.tax]) = [1 - [[tau].sub.r,i](1 - [p.sub.i]) - [[tau].sub.a,i] X [p.sub.i]]/(1 - [[tau].sub.a,i] X [p.sub.i]) (5)

AMT bonds vs. tax-exempt bonds:

E([R.sub.e])/E([R.sub.amt]) = 1 - [[tau].sub.a,i] X [p.sub.i] (6)

Taxable bonds vs. tax-exempt bonds:

E([R.sub.e])/E([R.sub.tax]) = 1 - [[tau].sub.r,i](1 - [p.sub.i]) - [[tau].sub.a,i] X [P.sub.i] (7)

Assuming the regular and AMT marginal tax rates are positive ([[tau].sub.r,i] > 0 and [[tau].sub.a,i] > 0), three predictions arise from these equations. First, the pretax return on tax-exempt bonds will be lower than the pretax return on taxable bonds ([R.sub.e] < [R.sub.tax]). Second, the pretax return on AMT bonds will be lower than that of taxable bonds ([R.sub.amt] < [R.sub.tax]) if the probability of being subject to the AMT ([p.sub.i]) is less than 1. Third, the pretax return on tax-exempt bonds will be lower than that of AMT bonds ([R.sub.e] < [R.sub.amt]) if the probability of being subject to the AMT ([p.sub.i]) is greater than zero. The pretax returns on tax-exempt and AMT bonds will be equal ([R.sub.e] = [R.sub.amt] if the probability of being subject to the AMT ([p.sub.i]) is zero.

I predict that investors will assess a positive, but less than 100 percent, probability of being subject to the AMT. The number of taxpayers subject to the AMT has been growing rapidly in recent years (Hube and Herman 1998; Steuerle 2001). However, taxpayers can implement tax-planning strategies to reduce the probability of being subject to the AMT. Due to the uncertainty regarding the applicability of the AMT on a year-by-year basis, it is unlikely that taxable investors assess either a 0 or a 100 percent probability of being subject to the AMT.

For a corporate investor to be indifferent between taxable bonds, AMT bonds, and tax-exempt bonds, the expected after-tax returns must also be equal. Unlike the individual investor, the expected after-tax return to a corporate investor from a tax-exempt bond also depends on the probability that the corporation is subject to the AMT. This is true because tax-exempt interest income goes into the calculation of adjusted current earnings (ACE). AMTI includes 75 percent of the excess of ACE over AMTI before the ACE adjustment. However, the effect of the AMT on after-tax returns from tax-exempt bonds is mitigated for corporate taxpayers because AMT paid in the current year may be claimed as a credit against the regular tax in some future year (I.R.C. [ss]53; Gramlich and Robbins 1993)(6). Thus, the true cost of paying AMT for the corporate investor is the difference between the tax paid in the current year and the present value of the tax credit to be received in future years. The corporate investor's after-tax ret urn on a tax-exempt bond is as follows.

Corporate investor in tax-exempt SALG bond:

E([r.sub.e,c] = E([R.sub.e])(1 - [p.sub.c]) + E([R.sub.e])(1 - 0.75 X [[tau].sub.a,c] X K)[p.sub.c]

= E([R.sub.e](1 - 0.75 X [[tau].sub.a,c] X K X [p.sub.c]) (8)

where K is a constant representing the difference between in the present value of one dollar of AMT paid currently and one dollar of AMT credit received at the end of n periods, the subscript c indicates the investor is a corporation, and all other variables are as previously defined. The K term ranges between 0 and 1. Let k be the discount rate per period and n be the number of periods between the AMT payment and the AMT credit receipt, then K = [1 - 1/[(1 + k).sup.n]].

The corporate investor's after-tax return on an AMT bond also depends on the probability of its being subject to the AMT as well as the timing of the future AMT tax credit. To a corporate investor, AMTI includes 75 percent of tax-exempt bond interest income and 100 percent of AMT bond interest income. The after-tax return to the corporate investor in an AMT bond is as follows.

Corporate investor in AMT bond:

E([r.sub.amt,c]) = E([R.sub.amt)(1 - [[tau].sub.a,c] X K X [p.sub.c]) (9)

where all variables are as previously defined.

Finally, the corporate investor's expected after-tax return from a taxable bond depends on whether the corporation pays tax under the regular tax system or is subject to the AMT as follows.

Corporate investor in taxable SALG bond:

E([r.sub.tax,c] = E([R.sub.tax])(1 - [[tau].sub.r,c])(1 -[p.sub.c]) + E([R.sub.tax])(1 - [[tau].sub.a,c] X K)[p.sub.c]

= E([R.sub.tax])[1 - [[tau].sub.r,c](1 - [p.sub.c]) + [[tau].sub.a,c] X K X [p.sub.c]] (10)

where all variables are as previously defined.

If the marginal investor in SALG bonds is a corporation and the expected after-tax returns are equal for that investor, then the following relations will hold.

Taxable bonds vs. AMT bonds:

E([R.sub.amt]/E([R.sub.tax]) = [1 - [[tau].sub.r,c](1 - [p.sub.c]) - [[tau].sub.a,c] X K X [p.sub.c]]/(1 - [[tau].sub.a,c] X K X [p.sub.c]) (11)

AMT bonds vs. tax-exempt bonds:

E([R.sub.e])/E([R.sub.amt]) = (1 - [[tau].sub.a,c] X K X [p.cub.c])/[1 - 0.75 * [[tau].sub.a,c] X K X [p.sub.c]] (12)

Taxable bonds vs. tax-exempt bonds:

E([R.sub.e])/E([R.sub.tax]) = [1 - [[tau].sub.r,c](1 - [p.sub.c]) - [[tau].sub.a,c] X K X [p.sub.c]]/[1 - 0.75 X [[tau].sub.a,c] X K X [p.sub.c]] (13)

Assuming the regular and AMT marginal tax rates are positive ([[tau].sub.r,c] > 0 and [[tau].sub.a,c] > 0), these equations lead to the same three predictions as those related to individual investors. First, the pretax return on AMT bonds will be lower than that of taxable bonds ([R.sub.amt] < [R.sub.tax]) as long as the probability of being subject to the AMT is less than 1. Second, the pretax return on tax-exempt bonds will be lower than that of AMT bonds ([R.sub.e] < [R.sub.amt]) as long as the probability of being subject to the AMT is greater than zero. The pretax return on tax-exempt bonds will equal that of AMT bonds ([R.sub.e] = [R.sub.amt]) if the probability of being subject to the AMT is zero. However, a taxable corporate investor is not likely to assess either a 0 or a 100 percent probability of being subject to the AMT because the applicability of the AMT is uncertain. Finally, the pretax return on tax-exempt bonds will be lower than that of taxable bonds ([R.sub.e] < [R.sub.tax]).

This analysis suggests that average pretax returns on AMT bonds will be higher than pretax returns on tax-exempt bonds and lower than pretax returns on taxable bonds if the marginal investor is either an individual or a corporation. (7) The hypotheses are formally stated as follows:

[H.sub.1] [R.sub.e] < [R.sub.amt]

[H.sub.2] [R.sub.e] < [R.sub.tax]

[H.sub.3] [R.sub.amt] < [R.sub.tax]

SAMPLE SELECTION AND RESEARCH DESIGN

Historical price information for SALO bonds is difficult to obtain. (8) The databases available to investors can only be searched for bonds that are actually available for sale at the time the search is conducted. This search provides information about bond features such as CUSIP number, tax status, bond rating, call provisions, sinking fund requirements, insurance, maturity, and current ask prices. After obtaining the bond CUSIP numbers from this search, historical bid price data can then be obtained from searching a bond dealer's database for specific bond CUSIP numbers. SALG bonds have $1,000 face values but are bundled for sale (usually in groups of $5,000 to $10,000) with each bundle having its own CUSIP number. As a result, one $10 million bond issue can have bonds listed under as many as 2,000 different CUSIP numbers. Bid prices are available for a given day only for those bond bundles that were available for sale on that day. Thus, for each bond price day in the sample, SALG bonds available for sale o n that day must be identified from a search conducted on or around that day. The sample for this study is therefore limited to those bonds that were available for sale around the time the searches for bond CUSIP numbers were performed (July 20, 2001 and May 1, 2002).

On July 20, 2001, I obtained a sample of CUSIP numbers for taxable SALG bonds and AMT bonds available for sale from Financial Independence Systems, Inc.'s web site at http://www.bondsearchl23.com. My sample includes all available SALG taxable bonds and AMT bonds, except zero coupon-rate bonds. I then selected a sample of tax-exempt bond CUSIP numbers that were matched by maturity with the SALG taxable bonds and AMT bonds. Matching by maturity date is done to mitigate differences in pretax bond yields associated with investors' expectations about future changes in interest rates. After identifying the sample of CUSIP numbers using the procedures above, I purchased the bond bid prices for the close of the trading day July 20, 2001 from Evaluation Services, Inc. The final sample for July 20, 2001 includes 53 taxable bonds, 354 AMT bonds, and 407 tax-exempt bonds.

A second sample was selected on May 1, 2002 to test whether the estimated implicit tax rates are stable across time. The Financial Independence Systems, Inc. database was no longer available on that date, so I obtained a sample of CUSIP numbers from Bond Express, Inc.'s web site at http://www.bondsonline.com. As in the previous sample, I first identified all the taxable SALG bonds and AMT bonds available for sale on May 1, 2002 and then selected a sample of tax-exempt bonds matched by maturity. After identifying the sample CUSIP numbers from this web site, I purchased the bond bid prices for the close of the trading day May 1, 2002 from Evaluation Services, Inc. The final sample for May 1, 2002 includes 36 taxable bonds, 246 AMT bonds, and 282 tax-exempt bonds.

The following model is estimated separately for each of the two days in the sample to test for differences in average risk-adjusted pretax yields across SALG bond types:

[YTM.sub.i] = [b.sub.0] + [b.sub.1][IAMT.sub.i] + [b.sub.2][ITAX.sub.i]+[b.sub.3][RATE.sub.i]+[b.sub.4][NR.sub.i]+[b.su b.5][CALL.sub.i]+[b.sub.6][SINK.sub.i]+[b.sub.7][INS.sub.i]+[b.sub.8] [YRS.sub.i]+[b.sub.9][STEX.sub.i]+[b.sub.10][STTAX.sub.i]+[e.sub.i] (14)

where:

[YTM.sub.i] = yield-to-maturity for bond issue i;

[IAMT.sub.i] = 1 if interest earned on bond issue i is tax-exempt for regular tax purposes but a tax preference for AMT purposes, 0 otherwise;

[ITAX.sub.i] = 1 if interest eamed on bond issue i is fully taxable for regular tax purposes, 0 otherwise;

[RATE.sub.i] = the Moody's or Standard & Poor's bond rating on a scale from 1 (least risky) to 9 (most risky) of bond issue i;

[NR.sub.i] = 1 if bond issue i is not rated, 0 otherwise;

[CALL.sub.i] = 1 if bond issue i is callable, 0 otherwise;

[SINK.sub.i] = 1 if bond issue i requires a sinking fund, 0 otherwise;

[INS.sub.i] = 1 if bond issue i is insured, 0 otherwise;

[YRS.sub.i] = years-to-maturity for bond issue i;

[STEX.sub.i] = 1 if bond issue i was issued in Iowa, illinois, Oklahoma, or Wisconsin, and is tax-exempt in that state, 0 otherwise; and

[STTAX.sub.i] = 1 if bond issue i was issued in Iowa, illinois, Oklahoma, or Wisconsin, and is taxable in that state, 0 otherwise.

Yield-to-maturity (YTM) is calculated as the discount required to make the present value of future expected pretax cash flows (biannual interest payments plus principal at maturity) equal to the current bid price. Using YTM implicitly assumes that the investor plans to buy and hold the bond until maturity. (9) RATE, NR, CALL, SINK, INS, and YRS are included in the model to control for nontax differences across SALG bond types. STEX and STTAX are included in the model to control for differences in implicit taxes arising from state income tax differences in Iowa, illinois, Oklahoma, and Wisconsin.

A positive relation is predicted between bond yields and bond ratings ([b.sub.3] > 0). In addition, bonds that are not rated are predicted to be more risky and, thus, require higher yields ([b.sub.4] > 0). Prior research also suggests that bonds with call options are more risky and may require higher yields ([b.sub.5] > 0). Sinking funds and insurance are expected to lower a bond's risk; however, these may be present only for those bonds that are higher risk in the first place. Therefore, no predictions are made regarding the signs on the coefficients for SINK and INS. Prior research suggests that bond risk premiums increase with the number of years-to-maturity. Therefore, the coefficient in YRS is expected to be positive ([b.sub.8] > 0). Finally, no predictions are made regarding the signs on the coefficients for STEX and STTAX.

I predict that risk-adjusted pretax bond yields on AMT bonds and taxable bonds are higher than those of tax-exempt bond yields ([b.sub.1] > 0, [b.sub.2] > 0) and that risk-adjusted pretax bond yields on AMT bonds are lower than those of taxable bonds ([b.sub.1] < [b.sub.2]). Using this research design, the [b.sub.0], [b.sub.1], and [b.sub.2] coefficients can also be used to measure the pretax yields for tax-exempt bonds ([b.sub.0]), AMT bonds ([b.sub.0] + [b.sub.1]), and taxable bonds ([b.sub.0] + [b.sub.2]), after subtracting the risk premiums associated with differences in bond ratings, call provisions, sinking fund requirements, insurance, and years-to-maturity These risk-adjusted yields can then be used to estimate the implicit taxes in tax-exempt and AMT bond yields. Implicit taxes are calculated as the yield on the fully taxable bond less the yield on the tax-favored bond (tax-exempt or AMT bond) divided by the yield on the fully taxable bond.

As discussed above, prior research has focused on measuring implicit taxes by comparing indexes of newly issued tax-exempt bond yields with those of U.S. Treasury securities or corporate bonds. These studies document implicit tax rates in very short-term tax-exempt bond yields that are close to the maximum statutory corporate tax rate but implicit tax rates in longer-term tax-exempt bond yields that are much lower. This finding is often referred to as the "muni puzzle." To provide additional evidence on the cause of the "muni puzzle," I examine whether the implicit taxes estimated using taxable SALG bonds as a benchmark are higher than those estimated using taxable U.S. Treasury security index yields as a benchmark with the following model:

[YTM.sub.nontax,i] = [b.sub.1][YTM.sub.tax,i] + [e.sub.i] (15)

where [YTM.sub.nontax,i] is the yield-to-maturity for tax-exempt SALG bond issue i and [YTM.sub.tax,i] is the yield-to-maturity for the benchmark taxable security (matched by maturity). In this model, [b.sub.1] can be interpreted as (1 - [tau]) where [tau] is the marginal investor's tax rate (Jordan and Pettway 1985). This model will be estimated for the SALG tax-exempt bonds that were matched by maturity with the SALG taxable bonds. The model is estimated two ways, using maturity-matched U.S. Treasury security index yields and maturity-matched SALG taxable bond yields as the benchmark taxable securities. (10) The implicit tax estimated using SALG taxable bonds as the benchmark is predicted to be larger than that obtained using U.S. Treasury security index yields as the benchmark.

RESULTS

Table 1 provides definitions for the variables that appear throughout the tables. Table 2 presents descriptive statistics for the sample bond issues broken down by sample date. As predicted, the average yields on tax-exempt bonds (4.975 and 4.118 percent for July 20, 2001 and May 1, 2002, respectively) are lower than those of AMT bonds (5.517 and 4.608 percent) and taxable bonds (6.737 and 5.795 percent). Furthermore, the average yields on AMT bonds (5.517 and 4.608 percent) are lower than those of taxable bonds (6.737 and 5.795 percent). However, there are significant nontax differences between the tax-exempt, AMT, and taxable bonds. The average bond ratings on taxable bonds (1.113 and 1.305) are lower than those of AMT bonds (1.737 and 1.975). On July 20, 2001, the average bond rating for taxable bonds (1.113) is also lower than that of tax-exempt bonds (1.700). The average years-to-maturity on taxable bonds (11.523 and 11.859 years) is lower than that of AMT bonds (16.929 and 17.337 years) and tax-exempt bonds (16.224 and 17.3 18 years).

As shown in Table 3, callable bonds represent 69.7 percent (76.2 percent), 70.6 percent (78.4 percent), and 33.9 percent (55.5 percent) of the tax-exempt, AMT, and taxable bonds for the July 20, 2001 (May 1, 2002) sample, respectively. Bonds with mandatory sinking fund requirements comprise 47.1 percent (47.5 percent), 41.8 percent (45.5 percent), and 47.1 percent (47.2 percent) of the tax-exempt, AMT, and taxable bonds for the July 20, 2001 (May 1, 2002) sample, respectively. Insured bonds represent 58.2 percent (60.6 percent), 39.2 percent (42.2 percent), and 56.6 percent (58.3 percent) of the tax-exempt, AMT, and taxable bonds for the July 20, 2001 (May 1, 2002) sample, respectively. Finally, bonds that are not rated represent 1.2 percent (1.4 percent), 5.9 percent (6.5 percent), and 20.7 percent (11.1 percent) of the tax-exempt, AMT, and taxable bonds for the July 20, 2001 (May 1, 2002) sample, respectively. Indicator variables are included in the multivariate regression model to control for mean differe nces in bond yields that are due to these bond features.

Table 4 presents the results of estimating Model (14) broken down by sample date. In prior research, implicit taxes estimated for longer-term tax-exempt bonds are lower than those estimated for shorter-term tax-exempt bonds. For this reason, Model (14) is estimated for the full July 20, 2001 sample and for a reduced sample where bonds maturing in less than two years are deleted. The May 1, 2002 sample has no bonds maturing in less than two years.

For the July 20, 2001 date, the model explains 61.84 percent of the variation in bond yields for the full sample and 62.81 percent for the reduced sample. The influence diagnostics indicate that multicollinearity is not present (variance inflation factors are all below 2 and the condition indices are all below 10). The White (1980) test indicates that heteroscedasticity is present ([chi square]-statistic = 74.74, p-value = 0.0211 for the full sample, [chi sqaure]-statistic = 70.62, p-value = 0.0438 for the reduced sample). Therefore, all t-statistics are calculated using the heteroscedasticity-consistent covariance matrix.

The model explains 52.09 percent of the variation in bond yields for the May 1, 2002 sample. As in the earlier sample, the variance inflation factors are all below 2 and the condition indices are all below 10, indicating that multicollinearity is not present. The White (1980) test indicates that heteroscedasticity is also present for this sample ([chi square]-statistic = 75.73, p-value = 0.0219) and, therefore, all t-statistics are calculated using the heteroscedasticity-consistent covariance matrix.

As predicted, bond yields are positively related to bond ratings ([b.sub.3] > 0), non-rated bonds have higher average yields ([b.sub.4] > 0), callable bonds have higher average yields ([b.sub.5] > 0), and yields increase with the years-to-maturity ([b.sub.8] > 0). In addition, bonds with sinking fund requirements ([b.sub.6] > 0) and insured bonds ([b.sub.7] > 0) have higher average yields. There are no significant state tax effects ([b.sub.9] = 0 and [b.sub.10] = 0). The average yields for AMT and taxable bonds are higher than the average yield for tax-exempt bonds ([b.sub.1] > 0 and [b.sub.2] > 0). Furthermore, the average taxable bond yield is higher than that of AMT bonds ([b.sub.2] > [b.sub.1]). These results are consistent with the hypotheses.

Table 5 presents estimates of the implicit taxes on tax-exempt and AMT bonds derived from the results of estimating Model (14). Scholes et al. (2002, 100-103) discuss the importance of adjusting for risk differences when estimating implicit taxes. They suggest that pretax risk premiums should be estimated first. The estimated pretax risk premiums should then be subtracted from gross pretax rates of returns. The resulting estimated risk-adjusted pretax returns should then be used to calculate implicit taxes on the tax-favored assets. They illustrate how the failure to use risk-adjusted pretax returns can lead to misleading estimates of implicit taxes and mask differences in the tax treatment of assets.

The control variables RATE, NR, CALL, SINK, INS, and YRS are included in Model (14) to remove the risk premiums associated with these bond features, while STEX and STTAX are included to remove the effects of state tax differences. The resulting [b.sub.0], [b.sub.1], and [b.sub.2] coefficients provide estimates of average risk-adjusted returns for tax-exempt bonds ([b.sub.0]), AMT bonds ([b.sub.0] + [b.sub.1]), and taxable bonds ([b.sub.0] + [b.sub.2]) after removing estimated risk premiums associated with differences in bond ratings, call features, sinking fund provisions, insurance, and years-to-maturity. Following the Scholes et al. (2002) example, these risk-adjusted returns are then used to calculate implicit taxes on tax-exempt and AMT bonds in Panel A of Table 5.

For the July 20, 2001 sample, the estimated implicit tax on AMT bonds ranges from 25.23 to 26.04 percent, while the estimated implicit tax on tax-exempt bonds ranges from 33.87 to 34.33 percent. The implicit tax on AMT bonds of 29.68 percent in the May 1, 2002 sample is somewhat higher than that of the July 20, 2001 sample. The implicit tax on tax-exempt bonds is also slightly higher at 35.27 percent.

The estimated implicit tax rate for tax-exempt bonds is very close to the maximum statutory tax rate for corporations of 35 percent in both samples. Contrary to prior research, this result holds for samples of bonds having longer-term maturities (greater than two years). Although the Miller (1977) hypothesis is not tested specifically in this study, these results are consistent with his predictions.

Panels B, C, and D of Table 5 present alternative estimates of the implicit taxes on tax-exempt and AMT bonds. To arrive at the estimates in Panels B and C, pretax returns are calculated by first summing the products of the sample means (Panel B) or sample medians (Panel C) of RATE, NR, CALL, SINK, INS, YRS, STEX, and STTAX by their respective Model (14) coefficients. This sum is then added to the [b.sub.0] coefficient as an estimate of average tax-exempt bond returns. Estimated average AMT and taxable bond returns are calculated by adding the coefficients [b.sub.2] and [b.sub.3], respectively, to the estimated average tax-exempt bond return. Implicit taxes are then calculated as the difference between the average taxable and tax-favored bond returns divided by the estimated average taxable bond return. Panel D presents the results of estimating implicit taxes using unadjusted pretax yields-to-maturity.

Estimated implicit taxes in Panels B, C, and D of Table 5 are much lower than those presented in Panel A. One interpretation of the alternative implicit tax estimates in Panels B and C is that they represent the implicit tax on the mean or median bond in the sample. However, both approaches assume that the average values for RATE, NR, CALL, SINK, INS, and YRS are constant across bond type. In my research design, this is equivalent to assuming that average risk premiums are equal across bond type. However, the descriptive statistics in Tables 2 and 3 indicate that the sample means and medians for RATE and YRS as well as the proportion of bonds having the bond features NR, CALL, SINK, and INS differ across bond type. These differences suggest that average risk premiums are not constant across bond type. Thus, a second interpretation of the implicit taxes in Panels B and C, is that they are misleading because the pretax returns are not properly adjusted for risk premium differences across bond types. In fact, th e implicit tax estimates from the mean and median approaches are very close to those obtained from using the unadjusted pretax yields-to-maturity as shown in Panel D.

The relative risk-adjusted pretax yields on tax-exempt bonds and AMT bonds are a function of the marginal investor's assessment of the probability of being subject to the AMT and the marginal investor's AMT rate. Equation (6) and Equation (12) present these relations for individual marginal investors and corporate marginal investors, respectively. The marginal investor's assessed probability of being subject to the AMT can be estimated by substituting the risk-adjusted pretax yields into these equations and solving for [p.sub.i] or [p.sub.c] using the appropriate statutory AMT rates. (11)

Using the July 20, 2001 full sample estimates and assuming the marginal investor is an individual, the assessed probability of being subject to the AMT is between 41.29 and 44.46 percent, depending on whether the individual's AMT rate is 26 or 28 percent. When the reduced sample estimates are used, this range is 40.05 to 43.13 percent. Using the May 1, 2002 sample estimates, these probabilities are lower (28.39 to 30.58 percent). There are no feasible values for [p.sub.c] and K in Equation (12) that would produce the observed spread between the pretax yields, suggesting that the marginal investors in SALG bonds are individuals.

The higher implicit tax on AMT bonds in the May 1, 2002 sample (compared to the July 1, 2001 sample) suggests that investors lowered their assessed probability of being subject to the AMT. In early 2002, Congress debated a proposed tax bill that would have repealed the corporate AMT (but not the individual AMT). Even though this proposal was not enacted, investors may have altered their beliefs about the possibility of the AMT being repealed in the future. Alternatively, this difference may be due to other changes in the relative risks between tax-exempt, AMT, and taxable SALG bonds that are not adequately controlled for in the model.

Under the Scholes and Wolfson (1992) framework, investors who do not pay the AMT would be expected to form a tax clientele for investing in AMT. In that case, there would be no significant difference in the pretax returns on tax-exempt bonds and AMT bonds. However, Scholes et al. (2002) illustrate how the joint presence of transaction costs and uncertainty with respect to future tax status can influence the formation of tax cienteles. In their example, the taxpayer must decide between investing in tax-exempt or taxable bonds over a three-year period, but is uncertain about his future tax rate (40 percent vs. 0 percent) because of the uncertain profitability of his investments already in place. The taxpayer could switch investments after the first year, but there is a significant annualized cost of switching. In their example, uncertainty regarding the future tax rate combined with significant switching costs changes the investor's optimal decision from that expected under certainty.

The evidence above indicates that the marginal investor in AMT bonds is an individual who assesses a positive probability (between 28 and 45 percent) of being subject to the AMT. This finding suggests that uncertainty regarding the applicability of the AMT, combined with transactions costs, impede the formation of a tax clientele composed of non-AMT-paying investors in AMT bonds.

Table 6 presents the results of estimating Model (15) for the pooled sample of the 89 taxable SALO bonds and their maturity-matched tax-exempt SALG bonds. In Panel A, U.S. Treasury security index yields (matched by maturity) are used as the benchmark taxable securities for estimating the implicit tax on the tax-exempt bonds. The [b.sub.1] coefficient of 0.858 indicates that the estimated implicit tax is 14.2 percent (1 -- 0.858). In Panel B, the taxable SALO bonds are used as the benchmark taxable securities for estimating the implicit tax on tax-exempt bonds. The [b.sub.1] coefficient of 0.65 1 indicates that the estimated implicit tax is 34.9 percent (1 -- 0.651). This result is consistent with the results from Model (14) above.

Chalmers (1998) regressed U.S. government secured tax-exempt SALG bonds on taxable U.S. Treasury securities yields and tenn-to-maturity. The SALG bonds he studies are noncallable and have essentially zero default risk. He reports a coefficient of 0.6361 (indicating an implicit tax of 36.9 percent) for the post-TRA 1986 period, but only when the term-to-maturity is included in the model. He interprets the statistically and economically large positive coefficient on term-to-maturity as indicating that default risk and call options do not provide a comprehensive explanation for the "muni puzzle."

To understand why implicit taxes are higher for my sample when taxable SALG bonds are used as a benchmark, I first calculate the difference between the taxable SALG bond yields and the maturity-matched U.S. Treasury security index yields. I then regress this difference on the bond features RATE, NR, CALL, and SINK. When INS, YRS, STEX, and STTAX are included in the regression, the model diagnostics indicate that severe multicollinearity is present. Multicollinearity is not present when INS, YRS, STEX, and STTAX are excluded from the model. However, the White (1980) test indicates that heteroscedasticity is present ([chi square]-statistic = 23.35, p-value = 0.0095) and, therefore, I calculate all t-statistics using the heteroscedasticity-consistent covariance matrix. The regression explains 50.17 percent of the difference between taxable SALG bond yields and maturity-matched U.S. Treasury security index yields.

Differences between taxable SALG bond yields and U.S. Treasury security index yields are significantly positively related to NR (coefficient = 2.290, t-statistic = 4.895) and SINK (coefficient = 0.943, t-statistic = 4.227) but are not related to RATE (coefficient = -0.0087, t-statistic = -0.058) and CALL (coefficient = -0.011, t-statistic = -0.049). In addition, there is a positive and significant mean difference of 0.550 (t-statistic = 2.592), indicating that a portion of this difference cannot be explained by the identified bond features. The higher yield on non-rated bonds is consistent with the results from Model (14) discussed above. The positive coefficient on SINK in this model, as well as in Model (14) above, suggest that bonds having mandatory sinking fund provisions are more risky and that this risk is not captured by bond ratings.

Finally, the mean difference between taxable SALG bond yields and U.S. Treasury security index yields (after controlling for NR, SINK, RATE, and CALL) suggests that part of the difference in yields between SALG bonds and U.S. Treasury security index yields is not due to the specific bond features identified. This portion of the difference may be due to differences in the market structures for these two types of securities. The SALG bond market is less centralized than the U.S. Treasury securities market. In addition, the bundling of SALG bonds into groups having different CUSIP numbers makes it difficult for investors to track a SALG bond's value over time, which increases the investor's information search costs. Investors may require higher yields on SALG bonds to offset these information search costs. These factors may explain the "muni puzzle" documented in prior research. Alternatively, this difference may be due to other risk differences that are not adequately controlled for in this model.

SUMMARY AND CONCLUSION

I examine risk-adjusted pretax yields on SALG bonds (tax-exempt bonds, AMT bonds, and taxable bonds) for evidence of implicit taxes. I find that the average risk-adjusted pretax yield on AMT bonds is higher than that of tax-exempt bonds and lower than that of taxable bonds. Implicit tax rates are estimated at 25.23 to 29.68 percent on AMT bonds and 33.87 to 35.27 percent on tax-exempt bonds. The results suggest that marginal investors in SALG bonds are individuals who assess a positive probability of being subject to the AMT (40.05 to 44.46 percent on July 20, 2001 and 28.39 to 30.58 percent on May 1, 2000).

This study provides evidence that asset prices are affected by the AMT system. This finding has implications for tax policymakers. If the federal government reduced the subsidy on state and local governments by subjecting a portion of SALG bond interest income to the regular income tax, then the state or local government would pay a higher pretax interest rate but the federal government would collect the difference as additional federal taxes. With the AMT system, the investor requires a higher pretax interest rate because he/she assesses a positive probability of being subject to the AMT. If the investor ultimately is not subject to the AMT for a given year, then the higher pretax interest rate paid by the state or local government is retained by the investor rather than collected by the federal government. Thus, the uncertainty regarding the applicability of the federal tax under the AMT system results in a decrease in the tax subsidy to state and local governments with no corresponding increase in federal tax revenues.

This study also provides evidence that marginal investors in AMT bonds are individuals who assess a positive probability of being subject to the AMT, indicating that investors not subject to the AMT are unable to form a tax clientele for investing in AMT bonds. This result is consistent with the Scholes et al. (2002) discussion of the joint effects of uncertainty regarding future tax status and transactions costs on the formation of tax clienteles. Consistent with their discussion, uncertainty regarding the applicability of the AMT, along with transactions costs from switching investments, appears to impede the formation of a non-AMT paying tax clientele for investing in AMT bonds.

Finally, this study provides evidence that using SALG taxable bond yields as a benchmark produces a higher estimated implicit tax rate in SALG tax-exempt bond yields than that obtained using U.S. Treasury security index yields as a benchmark. The difference between taxable SALG bond yields and maturity-matched U.S. Treasury security bond yields can be partially explained by risk (indicated by non-rated bonds and bonds having mandatory sinking fund provisions). However, the mean difference between taxable SALG bond yields and maturity-matched U.S. Treasury security bond yields cannot be explained by specific bond features identified in this study and may be due to higher information search costs in the SALG bond market. Alternatively, this difference may be due to differences in risk between SALG bonds and U.S. Treasury securities that are not adequately controlled for in my model.

The research methodology used in this study differs from prior research examining implicit taxes in tax-exempt bond yields in three ways. First, the data are yields-to-maturity determined from bid prices on specific SALG bonds rather than bond index yields. Second, SALG taxable bonds are used as benchmarks for measuring implicit taxes in SALG tax-exempt bond yields. Third, risk-adjusted pretax yields are estimated from a regression model that removes the estimated risk premiums associated with differences in bond ratings, call provisions, sinking fund requirements, insurance, and years-to-maturity. These risk-adjusted pretax yields are then used to estimate implicit taxes.

The advantage of this research methodology is that it allows for more controls for nontax differences between tax-exempt bonds and the taxable securities used as benchmarks for measuring implicit taxes. The disadvantage is that the data is limited to one or two trading days because of the difficulty in obtaining bond CUSIP numbers and pricing data. Future research should examine whether these results hold over longer time periods.
TABLE 1

VARIABLE DEFINITIONS


[YTM.sub.i]    = yield-to-maturity for bond issue i;

[nontax.sub.i] = subscript indicating bond issues that are
                 tax-exempt and not subject to the AMT;

[amt.sub.i]    = subscript indicating bond issues that are
                 tax-exempt but a tax preference for AMT;

[tax.sub.i]    = subscript indicating bond issues that
                 are fully taxable;

[RATE.sub.i]   = the Moody's or Standard & Poor's bond rating on
                 a scale from 1 (least risky) to 9 (most risky)
                 of bond issue i;

[YRS.sub.i]    = years to maturity for bond issue i;

[IAMT.sub.i]   = 1 if interest earned on bond issue i is
                 tax-exempt for regular tax purposes but a
                 tax preference for AMT, 0 otherwise;

[ITAX.sub.i]   = 1 if interest earned on bond issue i is
                 fully taxable for regular tax purposes,
                 0 otherwise;

[NR.sub.i]     = 1 if bond issue i is not rated, 0 otherwise;

[CALL.sub.i]   = 1 if bond issue i is callable, 0 otherwise;

[SINK.sub.i]   = 1 if bond issue i has a sinking fund provision,
                 0 otherwise;

[INS.sub.i]    = 1 if bond issue i is insured, 0 otherwise;

[STEX.sub.i]   = 1 if bond issue i was issued in Iowa,
                 Illinois, Oklahoma, or Wisconsin,
                 and is tax-exempt in that state,
                 0 otherwise; and

[STTAX.sub.i]  = 1 if bond issue i was issued in Iowa,
                 Illinois, Oklahoma, or Wisconsin, and is
                 taxable in that state, 0 otherwise.

TABLE 2

DESCRIPTIVE STATISTICS AND UNIVARIATE TESTS

                                  n    Mean   Std. Dev.   Q1    Median

Panel A: Descriptive Statistics
for sample of SALG Bonds
Available for Sale on July
20, 2001

[YTM.sub.nontax]                 407   4.975      1.227  4.267   5.100
[YTM.sub.amt]                    354   5.517      1.803  4.520   5.300
[YTM.sub.tax]                     53   6.737      1.534  5.925   6.452
[RATE.sub.nontax]                407   1.700      1.102  1.000   1.000
[RATE.sub.amt]                   354   1.737      1.342  1.000   1.000
[RATE.sub.tax]                    53   1.113      0.869  1.000   1.000
[YRS.sub.nontax]                 407  16.224      9.248  8.123  15.378
[YRS.sub.amt]                    354  16.929      9.202  8.458  17.296
[YRS.sub.tax]                     53  11.523      8.252  5.616   9.542

Panel B: Descriptive Statistics
for Sample SALG Bonds Available
for Sale on May 1, 2002

[YTM.sub.nontax]                 282   4.118      0.519  3.837   4.026
[YTM.sub.amt]                    246   4.608      0.974  4.009   4.278
[YTM.sub.tax]                     36   5.795      1.166  4.743   5.871
[RATE.sub.nontax]                282   1.450      0.843  1.000   1.000
[RATE.sub.amt]                   246   1.975      1.651  1.000   1.000
[RATE.sub.tax]                    36   1.305      0.888  1.000   1.000
[YRS.sub.nontax]                 282  17.318     11.138  8.838  16.515
[YRS.sub.amt]                    246  17.337      8.478  9.591  17.472
[YRS.sub.tax]                     36  11.859      7.578  7.257   8.921

                                   Q3

Panel A: Descriptive Statistics
for sample of SALG Bonds
Available for Sale on July
20, 2001

[YTM.sub.nontax]                  5.279
[YTM.sub.amt]                     5.753
[YTM.sub.tax]                     7.137
[RATE.sub.nontax]                 2.000
[RATE.sub.amt]                    2.000
[RATE.sub.tax]                    1.000
[YRS.sub.nontax]                 23.836
[YRS.sub.amt]                    24.340
[YRS.sub.tax]                    14.375

Panel B: Descriptive Statistics
for Sample SALG Bonds Available
for Sale on May 1, 2002

[YTM.sub.nontax]                  4.374
[YTM.sub.amt]                     4.886
[YTM.sub.tax]                     6.786
[RATE.sub.nontax]                 2.000
[RATE.sub.amt]                    3.000
[RATE.sub.tax]                    2.000
[YRS.sub.nontax]                 23.602
[YRS.sub.amt]                    24.016
[YRS.sub.tax]                    16.324

Panel C: Tests of Differences in Means and Medians

                                            July 20, 2001 Sample

                                            Mean           Median
                                         t-statistic     z-statistic

[YTM.sub.nontax] vs. [YTM.sub.amt]         4.78 *          6.36 *
[YTM.sub.amt] vs. [YTM.sub.tax]            4.68 *          7.16 *
[YTM.sub.nontax] vs. [YTM.sub.tax]         8.04 *          9.11 *
[RATE.sub.nontax] vs. [RATE.sub.amt]       0.41            0.76
[RATE.sub.amt] vs. [RATE.sub.tax]          4.49 *          3.45 *
[RATE.sub.nontax] vs. [RATE.sub.tax]       4.47 *          4.10 *
[YRS.sub.nontax] vs. [YRS.sub.amt]         1.05            1.02
[YRS.sub.amt] vs. [YRS.sub.tax]            4.04 *          3.88 *
[YRS.sub.nontax] vs. [YRS.sub.tax]         3.52 *          3.40 *

                                             May 1, 2002 Sample

                                            Mean           Median
                                         t-statistic     z-statistic

[YTM.sub.nontax] vs. [YTM.sub.amt]         7.33 *          6.48 *
[YTM.sub.amt] vs. [YTM.sub.tax]            6.65 *          6.01 *
[YTM.sub.nontax] vs. [YTM.sub.tax]         8.52 *          8.19 *
[RATE.sub.nontax] vs. [RATE.sub.amt]       4.50 *          2.80 *
[RATE.sub.amt] vs. [RATE.sub.tax]          3.69 *          2.09 **
[RATE.sub.nontax] vs. [RATE.sub.tax]       0.96            1.06
[YRS.sub.nontax] vs. [YRS.sub.amt]         0.02            0.66
[YRS.sub.amt] vs. [YRS.sub.tax]            3.67 *          3.57 *
[YRS.sub.nontax] vs. [YRS.sub.tax]         3.83 *          3.25 *

*, ** Significant at the 0.01 and 0.05 levels, respectively.

TABLE 3

BREAKDOWN OF SALG BOND FEATURES BY TAX TYPE

                     n       CALL         SINK          INS

Panel A: SALG Bonds
Available for Sale
on July  20, 2001

Tax-exempt           407  284 (69.7%)  192 (47.1%)  237 (58.2%)
AMT                  354  250 (70.6%)  148 (41.8%)  139 (39.2%)
Taxable               53   18 (33.9%)   25 (47.1%)   30 (56.6%)

  Total              814  552 (67.8%)  365 (44.8%)  406 (49.8%)

Panel B: SALG Bonds
Available for Sale
on May 1, 2002

Tax-exempt           282  215 (76.2%)  134 (47.5%)  171 (60.6%)
AMT                  246  193 (78.4%)  112 (45.5%)  104 (42.2%)
Taxable               36   20 (55.5%)   17 (47.2%)   21 (58.3%)

  Total              564  428 (75.8%)  263 (46.6%)  296 (52.4%)

                     Not Rated

Panel A: SALG Bonds
Available for Sale
on July  20, 2001

Tax-exempt             5  (1.2%)
AMT                   21  (5.9%)
Taxable               11 (20.7%)

  Total               37  (4.5%)

Panel B: SALG Bonds
Available for Sale
on May 1, 2002

Tax-exempt             4  (1.4%)
AMT                   16  (6.5%)
Taxable                4 (11.1%)

  Total               24  (4.2%)

TABLE 4

REGRESSION ANALYSIS OF SALG BOND YIELDS

Model (14): [YTM.sub.i] = [b.sub.0] + [b.sub.1][IAMT.sub.i] +
[b.sub.2][ITAX.sub.i] + [b.sub.3][RATE.sub.i] + [b.sub.4][NR.sub.i] +
[b.sub.5][CALL.sub.i] + [b.sub.6][SINK.sub.i] + [b.sub.7][INS.sub.i] +
[b.sub.8][YRS.sub.i] + [b.sub.9][STEX.sub.i] + [b.sub.10][STTAX.sub.i] +
[e.sub.i]

                                           Full Sample
                                          July 20, 2001

                        Pred.            Coeff.          t-statistic

Intercept                >0               2.738           19.696 *
IAMT                     >0               0.358            5.586 *
ITAX                     >0               1.402            6.991 *
RATE                     >0               0.552            8.368 *
NR                       >0               5.002            8.239 *
CALL                     >0               0.462            6.093 *
SINK                      ?               0.307            3.722 *
INS                       ?               0.419            4.917 *
YRS                       +               0.031            5.883 *
STEX                      ?               0.195            0.445
STTAX                     ?               0.381            1.592
Adj. [R.sup.2]                           0.6184
n                                           814

[H.sub.A]: IAMT < ITAX            t-statistic = 5.085 *


                              YRS [greater than or equl to] 2
                                       July 20, 2001

                               Coeff.             t-statistic

Intercept                       2.858              21.240 *
IAMT                            0.361               5.765 *
ITAX                            1.494               7.958 *
RATE                            0.576               8.868 *
NR                              5.115               8.254 *
CALL                            0.409               5.558 *
SINK                            0.362               4.607 *
INS                             0.429               5.175 *
YRS                             0.023               4.635 *
STEX                            0.176               0.405
STTAX                           0.309               1.305
Adj. [R.sup.2]                 0.6281
n                                 790

[H.sub.A]: IAMT < ITAX  t-statistic = 5.836 *


                                    Full Sample
                                    May 1, 2002

                               Coeff.          t-statistic

Intercept                       3.012           27.203 *
IAMT                            0.260            5.620 *
ITAX                            1.641           10.154 *
RATE                            0.329            7.674 *
NR                              2.145            7.666 *
CALL                            0.261            3.446 *
SINK                            0.127            1.851 ***
INS                             0.302            4.391 *
YRS                             0.009            2.144 **
STEX                           -0.302           -1.317
STTAX                          -0.029           -0.322
Adj. [R.sup.2]                 0.5209
n                                 564

[H.sub.A]: IAMT < ITAX  t-statistic = 7.949 *


*, **, *** Significant at the 0.01, 0.05 and 0.10 levels, respectively,
based on two-sided t-tests.

TABLE 5

ESTIMATES OF IMPLICIT TAXES FROM MODEL (14) RESULTS

                                   Full          YRS          Full
                                  sample   [greater than or  Sample
                                   July      equal to] 2       May
                                 20, 2001   July 20, 2001    1, 2002

                                    %             %             %

Panel A: Using [b.sub.0],
[b.sub.1], and [b.sub.2] Only

[T.sub.amt,implicit]              25.23         26.04         29.68
[T.sub.e,implicit]                33.87         34.33         35.27

Panel B: setting All Variables
to the Sample Means

[T.sub.amt,implicit]              16.11         17.10         23.56
[T.sub.e,implicit]                21.64         22.55         27.99

Panel C: setting All Variables
to the Sample Medians

[T.sub.amt,implicit]              18.53         18.38         24.23
[T.sub.e,implicit]                24.88         24.23         28.79

Panel D: Using Raw Yields-to-
Maturity

[T.sub.amt,implicit]              18.11         18.87         20.48
[T.sub.e,implicit]                26.15         26.60         28.94

TABLE 6

REGRESSION ANALYSIS OF TAX-EXEMPT SALG BOND YIELDS ON MATCHED TREASURY
SECURITY AND TAXABLE SALG BOND YIELDS

Model (15): [YTM.sub.nontax,i] = [b.sub.1][YTM.sub.tax,i] + [e.sub.i]

                                                            Adj.
                        Prediction   Coeff.  t-statistic  [R.sup.2]  n

Panel A: [YTM.sub.tax]
is U.S. Treasury
Securities Matched
by Maturity

[YTM.sub.tax]           (1 - [tau])  0.858     60.98 *     0.9763    89
[[tau].sub.e,implicit]     14.2%

Panel B: [YTM.sub.tax]
is Taxable SALG
Bonds Matched
by Maturity

[YTM.sub.tax]           (1 - [tau])  0.651     39.53 *     0.9461    89
[[tau].sub.e,implicit]     34.9%

* Significant at the 0.01 level, based on two-sided t-tests.


I thank participants at research workshops at the University of Missouri, the 2002 AAA Midwest Regional meeting, the 2002 AAA Annual Meeting, Tom Omer, Michelle Hanlon, and an anonymous reviewer for their helpful comments. The University of Missouri, College of Business Research Incentive Fund provided funding for this project.

Submitted: December 2001

Accepted: September 2002

(1.) See Chalmers (1998) for a comprehensive review of prior research examining the "muni puzzle."

(2.) In 1998, the Joint Committee on Taxation (JCT) estimated the number of taxpayers affected by the AMT would grow from 134,000 in 1988 to 8.8 million by 2008 (Hube and Herman 1998). After the most recent tax cuts, the JCT estimates the number of taxpayers subject to the AMT will grow to 35 million by 2010 (Steuerle 2001).

(3.) See Scholes and Wolfson (1992), Scholes et al. (2002), and Shackelford and Shevlin (2001) for detailed discussions of the implicit tax theory and for a review of prior empirical research.

(4.) Refunding bonds are private activity bonds issued after August 7, 1986 to refund other bonds originally issued prior to August 7, 1986. Thus, previously tax-exempt bonds can be refunded after August 7, 1986 and remain free of the AMT taint. Qualifying I.R.C. [ss]501(c)(3) bonds are private activity bonds with proceeds that provide property to be owned by an I.R.C. [ss]501(c)(3) organization (or a governmental unit) and that meet other restrictions [I.R.C. [section]145].

(5.) Individuals may be able to claim a future credit for a portion of the AMT paid in the current year [I.R.C. [section]53(d)(1)(B)(i) and (ii)]. This portion is determined by calculating the amount of AMT that would have been paid if the only adjustments and preferences were those specified in I.R.C. [section]53(d)(1)(B)(ii). When this "as if" AMT paid is less than the actual AMT paid, the difference between the two is the portion of the current year AMT paid that can be claimed as a future credit. The way the calculation works, an individual cannot claim a future credit for AMT arising from the items specified in I.R.C. [section]53(d)(1)(B)(ii), including AMT bond interest and certain itemized deductions. As a result, only a small portion of the AMT paid by an individual (the amount arising from certain timing differences) can be claimed as a future credit.

(6.) For a corporation, I.R.C. [section]53(d)(1)(B)(iv) provides that the full amount of any AMT paid in the current year is available as a credit in future years (including AMT arising from tax-exempt or AMT bond interest).

(7.) This analysis essentially assumes that bonds are issued at par and ignores market premiums and discounts. As discussed in the second section, a taxpayer investing in taxable bonds has the option of recoganizing any market discount or deducting any market premium over the life of the bond. If this election is not made, then differences will arise between the timing of the receipt of the income and the taxation of the income. Furthermore, an investor in a tax-exempt market discount bond will be subject to tax on the market discount as ordinary income at maturity.

(8.) studies examining tax-exempt bonds have avoided this problem by using bond index yield data rather than individual bond yield data. However, that approach does not allow for controls for specific bond features such as call options, insurance, and mandatory sinking fund requirements.

(9.) As previously discussed, gains and losses at maturity or on the disposition of bonds before maturity are generally capital gains and losses; however, any portion of the gain attributable to accrued market discount is ordinary income. Thus, investors cannot convert ordinary income into capital gains by selling the bonds prior to maturity.

(10.) U.S. Treasury security index yields were obtained from the Federal Reserve Bank of St. Louis website at http://www/stls.frb.org. The U.S. Treasury security index yields are described on the web site as follows: "Yields on Treasury securities at constant, fixed maturity are constructed by the Treasury Department, based on the most actively traded marketable Treasury securities. Yields on these issues are based on composite quotes reported by U.S. government securities dealers to the Federal Reserve Bank of New York. To obtain the constant maturity yields, personnel at the Treasury construct a yield curve each business day and yield values are then read from the curve at fixed maturities."

(11.) The statutory AMT rates for individuals are 26 percent (for AMTI of $175,000 or less) and 28 percent (for AMTI greater than $175,000). The statutory AMT rate for corporations is 20 percent.

REFERENCES

Arak, M., and K. Guentner. 1983. The market for tax-exempt issues: Why are the yields so high? National Tax Journal 37 (2): 145-161.

Atwood, T. 2002. Public utility old money preferred stock. The Journal of the American Taxation Association (Spring): 1-16.

Buser, S., and P. Hess. 1986. Empirical determinants of the relative yields on taxable and tax-exempt securities. Journal of Financial Economics 17: 335-355.

Chalmers, J. 1998. Default risk cannot explain the muni puzzle: Evidence from municipal bonds that are secured by U.S. Treasury obligations. The Review of Financial Studies 11(2): 281-308.

Erickson, M., and E. Maydew. 1998. Implicit taxes in high dividend yield stocks. The Accounting Review (October): 435-458.

Gramlich, J., and E. Robbins. 1993. Alternative minimum tax and effective returns from municipal bonds. Journal of Applied Business Research 9 (4): 97-103.

Guenther, D. 1994. The relation between tax rates and pretax returns: Direct evidence from the 1981 and 1986 tax rate reductions. Journal of Accounting and Economics 18 (3): 379-393.

Hube, K., and T. Herman. 1998. You may be richer than you thought (and poorer, thanks to a "stealth tax"). Wall Street Journal (December 17): Cl.

Jordan, B., and R. Pettway. 1985. The pricing of short-term debt and the Miller hypothesis: A note. Journal of Finance 40 (2): 589-594.

Miller, M. 1977. Debt and taxes. Journal of Finance 32: 261-271.

Poterba, J. 1986. Explaining the yield spread between taxable and tax-exempt bonds. In Studies in State and Local Public Finance, edited by H. Rosen, 5-48. Chicago, IL: University of Chicago Press.

Scholes, M., and M. Wolfson. 1992. Taxes and Business Strategy. Englewood Cliffs, NJ: Prentice Hall.

-----, -----, M. Erickson, E. Maydew, and T. Shevlin. 2002. Taxes and Business Strategy. Upper Saddle River, NJ: Prentice Hall.

Shackelford, D. 1991. The market for tax benefits. Journal of Accounting and Economics 14 (2): 117-145.

-----, and T. Shevlin. 2001. Empirical tax research in accounting. Journal of Accounting and Economics 31: 321-387.

Skelton, J. 1983. Relative risk in municipal and corporate debt. Journal of Finance 38 (2): 625-634.

Steuerle, G. 2001. Moving beyond the fight over the alternative minimum tax. Tax Notes 91 (June 18): 2067- 2068.

Stock, D. 1994. Term structure effects on default risk premia and the relationship of default-risky tax-exempt yields to risk-free taxable yields: A note. Journal of Banking and Finance 18 (6): 1185-1203.

Trzcinka, C. 1982. The pricing of tax-exempt bonds and the Miller hypothesis. Journal of Finance 37 (4): 907-923.

White, H. 1980. A heteroscedasticity-consistent covariance matrix estimator and a direct test for heteroscedasticity. Econometrics 48: 817-838.

Yawitz, J., K. Maloney, and L. Ederington. 1985. Taxes, default risk and yield spreads. Journal of Finance 40 (4): 1127-1140.

T. J. Atwood is a Visiting Assistant Professor at the University of illinois at Urbana--Champaign.
COPYRIGHT 2003 American Accounting Association
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 2003 Gale, Cengage Learning. All rights reserved.

 
Article Details
Printer friendly Cite/link Email Feedback
Title Annotation:alternative minimum tax
Author:Atwood, T.J.
Publication:Journal of the American Taxation Association
Geographic Code:1USA
Date:Mar 22, 2003
Words:13249
Previous Article:ATA Tax Manuscript Award.
Next Article:Using declarative knowledge to improve information search performance.
Topics:

Terms of use | Privacy policy | Copyright © 2018 Farlex, Inc. | Feedback | For webmasters