National Tax Journal Vol 50 no. 2 (June 1997) pp. 315-20

INDEXED BONDS, EXPECTED INFLATION, AND TAX CLIENTELE BIAS

INDEXED BONDS, EXPECTED INFLATION, AND TAX CLIENTELE BIAS DAVID N. F. BELL, * ERIC J. LEVIN, * & ROBERT E. WRIGHT

**

Abstract – The U.S. Treasury Department has recently issued inflationindexed bonds whose yields may be used to provide bond market–based measures of expected inflation. This paper suggests that the U.S. tax treatment of the inflation indexation uplift on the principal may create a “tax clientele bias,” which could cast doubt on the interpretation of the yield gap between indexed and conventional bonds as a market measure of expected inflation. This problem is discussed in the context of the United Kingdom, a country where inflation-indexed bonds have been issued for the past 14 years.

be held in January 1997. This follows statements recently expressed by The Federal Reserve System concerning the advantages of issuing “indexed bonds”, that is, bonds whose coupon and principal are uplifted at regular intervals using the consumer price index in order to compensate for the loss of purchasing power caused by inflation (U.S. Department of the Treasury, 1996; Greenspan, 1992; Hetzel, 1992; U.S. House Committee on Government Operations, 1992). The existence of indexed and conventional bonds would generate an observable difference between the yield on indexed bonds and the yield on conventional bonds, which could then be used to provide market-based measures of expected inflation. The term structure of expected inflation, which shows how financial markets believe that inflation is going to change over different future points in time, is of special interest. The reason for this is that expected changes in inflation are particularly relevant for policies concerned with inflation targeting. In principle, the term structure of expected inflation could be inferred from the term structure of the gap between the yield paid on conven-

INTRODUCTION In December 1996, the U.S. Treasury Department announced that the first inflation-indexed security auction would

*

Department of Economics, University of Stirling, Stirling, Scotland FK9 4LA United Kingdom. ** Department of Economics, University of Stirling, Stirling, Scotland, FK9 4LA United Kingdom, and Centre for Economic Policy Research, London, England W1X ILB.

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tional bonds and the yield paid on bonds indexed to the price level. Therefore, the issuance of indexed bonds should provide valuable information and assist in the formulation of effective monetary and fiscal policy.

the market and the tax specific yield curve for zero tax-rate payers at the long end of the market. The U.S. tax legislation currently treats a capital gain from a rise in bond prices as imputed income, which is taxable, and this principle has been extended to apply to indexed bonds (U.S. Department of the Treasury, 1997). This means that any nominal increment in the value of the principal caused by an inflation indexation uplift is taxable. However, such a taxable increase in the value of the principal would not be attributable to any real gain but only to inflation. Insofar as this lowers the value of inflation-indexed bonds to a taxpayer but not to a nontaxpayer, high taxpayers may be reluctant to hold inflationindexed bonds at a price at which nontaxpayers would be willing to hold indexed bonds. This, in turn, implies that, if nontaxpayers determine the price of indexed while taxpayers determine the price of conventional bonds, a “U.S. tax clientele” may be created, which could distort bond-based measures of expected inflation for the United States.

Greenspan (1992) indicates a number of difficulties that arise in the practical application of accurately measuring the term structure of expected inflation using indexed and conventional bonds. One potentially serious problem relates to taxation. More specifically, it is now well known that, when different marginal tax rates apply to different bondholders, there is a unique term structure of interest rates for each tax class of bondholder (see, for example, Schaefer, 1981). The problem in the United Kingdom is that, as high marginal tax-rate payers are exempted from taxation on capital gain, they have a tax avoidance incentive to congregate at the short end of the market (the short end of the market includes those bonds with a short period remaining before the redemption date and consequently few taxable coupon payments) in order to enjoy a higher proportion of their return in the form of tax free capital gain.

With this in mind, the purpose of this paper is to examine this problem based on the experience of the United Kingdom, a country where indexed bonds have been issued for the past 14 years. The analysis shows that, in the U.K. case, nontaxation of capital gain on government bonds is likely to result in a tax clientele effect, whereby high marginal rate taxpayers congregate at the short end of the market. This, in turn, could cause an upward bias in the slope of observed term structure of interest rates for conventional bonds which would thwart attempts to measure accurately the term structure of expected inflation in the United Kingdom.

High marginal tax-rate payers, however, also have lower discount rates along the term, which implies lower yield curves. If this were not the case, then low tax-rate payers would value all positive coupon bonds more highly than high tax-rate payers, bidding them out of the market altogether. This creates a problem of observational equivalence. It would be difficult to know whether the observed term structure of the yield curve gap between indexed and conventional bonds reflects (1) the term structure of expected inflation or (2) the difference between the tax specific yield curve for high tax-rate payers at the short end of 316

National Tax Journal Vol 50 no. 2 (June 1997) pp. 315-20

INDEXED BONDS, EXPECTED INFLATION, AND TAX CLIENTELE BIAS

Somewhat paradoxically, in the United States, the taxation of the inflation uplift in the value of the principal for indexed securities (i.e., capital gain) could also result in a tax clientele. More specifically, this tax clientele arises from nontaxpayers who determine the price of indexed securities and from taxpayers who determine the price of conventional securities. This could cause a bias in the observed yield gap between indexed and conventional securities, which would also thwart attempts to accurately measure expected inflation.

Each of these propositions is discussed sequentially below. High Taxpayers Must Have Lower Yield Curves Than Low Taxpayers Savings (S) are a positive function of the interest rate (i) and income (Y). Figure 1 shows that it is a consequence of the tax system, not differences in individuals’ utility functions, that causes high marginal rate taxpayers to have a lower discount rate. Low income zero rate taxpayers’ aggregate saving function is shown as SYZ , and the gross market interest rate, i, elicits SZ savings. For high income savers who face a positive marginal tax rate t, the aggregate saving function is shown as SYH, and the net 2 interest rate i(1 – t) elicits SH saving. The high income taxpayers adjust to the positive marginal tax rate by saving less 2 at a lower net interest rate. Therefore, high income taxpayers have a lower term structure of interest rates.

THE PROBLEM The problem in the United Kingdom derives from three propositions: (1) High taxpayers must have lower yield curves than low taxpayers; (2) Short (long) bonds are more attractive to high (low) taxpayers; and (3) The relevant tax rate for each bond traded is unobservable.

FIGURE 1.

This explains why high marginal taxpayers are willing to bid the price of

Savings Functions for Zero Rate and High Rate Taxpayers

1

1

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low coupon bonds above the price that zero taxpayers are willing to pay. This is shown in Figure 2. If both groups had the same discount rates, zero taxpayers would value all government bonds with positive coupons higher (line AC in Figure 2) than taxpayers who would be driven out of the market altogether (line AA in Figure 2). The coexistence of both groups in the market for bonds with a positive coupon is a consequence of the fact that high marginal taxpayers have a lower discount rate (line BB in Figure 2).

definition be willingly held by both clienteles. These bonds would trade at a single price, even though their net coupons would differ. In this case, the no-arbitrage condition would be maintained by the higher tax clientele 3 applying a lower discount rate. The first stage in our argument is that, at all points along the term structure, high taxpayers must have a lower discount rate than low taxpayers. Short (Long) Bonds Are More Attractive to High (Low) Taxpayers

This also explains that, if there were no gaps along the term and all possible coupon bonds existed, there would be some bond(s) that, lying at the margin between two tax clienteles, would by

FIGURE 2.

Annual returns in the form of capital gain for high rate taxpayers in the United Kingdom are exempt from tax. Consequently, high tax-rate payers in

Present Value of a Bond for Zero Rate and High Rate Taxpayers

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INDEXED BONDS, EXPECTED INFLATION, AND TAX CLIENTELE BIAS

the United Kingdom “prefer” short bonds with low coupons because these maximize the tax free annual return. All bonds whose coupon rate is below the discount rate will trade below £100. For such bonds, the shorter is the period to redemption, the greater will be the tax free annual capital gain. Likewise, holding the period to redemption constant, the lower is the coupon below the discount rate, the higher will be the tax free annual capital gain. Therefore, short low coupon bonds are more financially attractive to high tax-rate payers and long high coupon bonds are more attractive to low tax-rate payers.

estimate of the term structure of interest rates, it would be necessary to build this relationship into the model to be estimated. However, there is a fundamental problem of identification because it is not possible to allocate an observed slope in the term structure between interest rates altering as a function of term and tax rates altering as a function of term. The identification problem can be seen in the bond price equation below, where P is the price of a bond with coupon C and redemption value R maturing at time T, rtTj is the yield at date t for the jth pure discount bond with maturity Tj, and π is the unobservable relevant marginal tax rate for trades in bond j at time t:

The Relevant Tax Rate for Each Bond Traded Is Unobservable Currently, in the United Kingdom, there are five different rates of income tax. The complication that arises because of differing tax rates is that the relevant marginal tax rate for a particular bond may change from one transaction to another. Tax rates refer to investors, not to a particular bond or group of bonds. Clearly, it is extremely difficult if not impossible to obtain such information, because the relevant tax rate for any given bond could change quite frequently, depending on the characteristics of the shifting population of investors trading. Therefore, the relevant tax rate for each bond traded is unobservable.

1 PjtTj =

Cj (1 – πj) t+1 t

(1 + r (πj)) +

+

Cj (1 – πj) (1 + rtt+2(πj))2

Cj (1 – πj) + Rj (1 + rtt+Tj(πj))Tj

+ ...

+ ujt .

In the bond price equation above, both the net coupon and the discount rate depend on the unobserved tax rate. This implies that there are different combinations of tax and discount rates across the term, which are consistent with a given observed term structure. As an example, an observed upward slope in the term structure is consistent with either a single tax rate together with a genuine upward slope in the term structure or a number of tax rates together with a flat term structure. There is a problem of observational equivalence, which cannot be resolved by estimation using data on the current set of government bonds available.

IMPLICATIONS The combination of these three propositions suggests that an observed upward slope in the term structure of interest rates may not imply rising expected inflation but rather that high taxpayers congregate at the short end of the market, and high taxpayers have lower interest rates. In order to remove this tax clientele induced upward bias in any 319

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different from the “UK tax clientele effect,” will be created, which could cast doubt on the interpretation of the yield gap as a market measure of expected inflation. However, in the United States, the tax clientele effect would be weakened to the extent that high rate taxpayers can postpone taxation until realization and are excused from taxation at death. When more information relating to indexed bonds becomes available, serious research aimed at trying to evaluate the size of this tax clientele bias needs to be carried out.

Conclusions Tax exemption on capital gains in the United Kingdom leads high marginal rate taxpayers to congregate at the short end of the market for government bonds. Necessarily, these taxpayers have lower discount rates. Together, these two factors lead to an upward slope in the observed term structure of interest rates, which might be incorrectly interpreted as a market forecast that inflation is expected to rise in the future. The U.K. experience is relevant for the U.S. current interest in issuing indexed bonds in order to obtain a bond marketbased forecast of expected inflation. The United States also faces a potential tax clientele problem. However, the mechanisms generating this problem are slightly different. Capital gain in the United States is treated as taxable income, and, consequently, there is no reason for zero rate taxpayers to be displaced from the short end of the conventional bond market. However, the decision to tax the inflation component on the principal for inflationindexed securities creates another problem.

ENDNOTES The comments of the editor and the anonymous referees were most helpful. Of course, full responsibility for all remaining errors and omissions are the authors.

REFERENCES Greenspan, Alan . “Statement Before the Commerce, Consumer and Monetary Affairs Subcommittee of the House Committee on Government Operations.” Federal Reserve Bulletin 78 No. 8 (August, 1992): 603–7. Hetzel, Robert L . “Indexed Bonds as an Aid to Monetary Policy.” Federal Reserve Bank of Richmond Economic Review 78 No. 1 (January/ February, 1992): 13–23. Schaefer, Stephen M . “Measuring a TaxSpecific Term Structure of Interest Rates in the Market for British Government Securities.” Economic Journal 91 No. 362 (June, 1981): 415– 38.

This problem arises because the ratio of the net redemption yield for nontaxpayers to the redemption yield for taxpayers for inflation-indexed securities, “r ZI L / r TI L,” will be considerably higher compared with conventional securities, “r NZ / rTN ,“ during periods of positive expected inflation. However, if r ZI L / r TI L > r NZ / r TN , then zero rate taxpayers are more likely to hold and determine the price of indexed securities, while high taxpayers are more likely to hold and determine the price of conventional securities. Therefore, a “U.S. tax clientele effect,” albeit

U.S. Congress. House. Committee on Government Operations. Fighting Inflation and Reducing the Deficit: The Role of InflationIndexed Government Bonds. Washington, D.C., October 29, 1992. U.S. Department of the Treasury. Statement of Treasury Secretary Robert E. Rubin: Inflation Indexed Bonds Press Conference. Washington, D.C., May 16, 1996. U.S. Department of the Treasury. “InflationIndexed Debt Instruments.” Federal Register 62 No. 3 (January, 1997): 615–21.

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